Economic Modelling 33 (2013) 1–7

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Economic Modelling

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Forecasting the yield curve and the role of macroeconomic informationin Turkey

Huseyin KayaBahcesehir University, I.I.B.F Ciragan Cad. Besiktas, Istanbul,Turkey

E-mail address: huseyin.kaya@bahcesehir.edu.tr.

0264-9993/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.econmod.2013.03.013

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 21 March 2013Available online xxxx

JEL classification:C33C53E43E44

Keywords:Yield curveForecastingMacroeconomic variablesDNSATSM

In this study we investigate the yield curve forecasting performance of Dynamic Nelson–Siegel Model (DNS),affine term structure VAR model (ATSM VAR) and principal component model (PC) in Turkey. We also inves-tigate the role of macroeconomic variables in forecasting the yield curve. We have reached numbers ofimportant results: 1—Macroeconomic variables are very useful in forecasting the yield curve. 2—The forecast-ing performances of the models depend on the period under review. 3—Considering the structural breakwhich associates with change in monetary policy leads models to produce better forecasts than the randomwalk. 4—The role of exchange rate should not be ruled out in forecasting the yield curve in an emergingmarket like Turkey.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Forecasting the term structure of interest rates has long been ofinterest to financial economists, central bankers and portfolio man-agers since it plays a crucial role in pricing financial assets and theirderivatives, managing financial risk, allocating, portfolios, structuringfiscal debt, conducting monetary policy, and valuing capital goods(Christensen et al., 2011). As the term structure of interest ratescarries important information about the monetary policy and themarket risk factors, numbers of theoretic and empirical researchesfor forecasting the yield curve are being conducted. However, asargued in Exterkate (2008), forecasting the term structure of interestrates is not an easy task and many attempts to outperform a simplerandom walk in forecasting the yield curve have failed.

The literature on the modeling of the yield curve is mainly domi-nated by the no-arbitrage affine term structure models (ATSM). Thisliterature is started by Vasicek (1977) and Cox et al. (1985). Duffieand Kan (1996) characterize and Dai and Singleton (2000) classifythese models. Vasicek (1977) and Cox et al. (1985) propose a singlefactor model, an instantaneous short rate that drives the market,however, it produces poor yield curve forecasts (Duffee, 2002).Chen and Scott (1993) argue that one factor is not appropriateto characterize the entire yield curve and propose multifactor

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generalization of the CIR (Cox, Ingersoll and Ross) model. On theother hand, Duffie and Kan (1996) characterize the exponentialterm structure models which are a class of models that the yieldsare an affine function of the latent state variables. Following Duffieand Kan (1996), these types of affine models become particularlypopular (Christensen et al., 2011). Dai and Singleton (2000) analyzethe affine term structure models and show that the yield curve move-ments can be reduced to three factors.

In a seminal paper, Ang and Piazzesi (2003) describe the jointdynamics of the term structure of interest rates and macroeconomicvariables by an ATSM VAR. By assuming that the state vector followsa Gaussian VAR, they show that imposing the no-arbitrage restric-tions and incorporating macroeconomic variables increase the fore-casting performance of the VAR. As they bring in the picture therole of macroeconomic variables in dynamics of the yield curve move-ment, their study fills such a very important gap that the ATSM liter-ature does not mention the role of macroeconomic variables so far.For 1-month ahead forecast horizon, their model shows better perfor-mance than the random walk but with a small gain.

An alternative approach is proposed by Nelson and Siegel (1987).This approach uses statistical techniques to explain the movement inthe yield curve and becomes very popular among practitioners andcentral banks. Diebold and Li (2006) extend the yield curve modelof Nelson and Siegel (1987) to the dynamic form and show that theDynamic Nelson–Siegel Model (DNS) compared to the many bench-mark models including the ATSM and the random walk, produces

2 H. Kaya / Economic Modelling 33 (2013) 1–7

superior out of sample forecasts especially for one year ahead forecasthorizon. Diebold et al. (2006) extend the model of Diebold and Li(2006) by incorporating macroeconomic variables. While Dieboldand Li (2006) use a two step approach, Diebold et al. (2006) proposea one step approach using the state space framework. They argue thata one step approach should improve out of sample forecasts, however,they did not provide and forecast result. Yu and Zivot (2011) investigateout of sample forecasting performance of the one step and two stepDNSmodels and find that a one step approach does not improve forecastingperformance. Instead, a two step approach provides more accurateforecasts.

To assess the relative importance of no-arbitrage restrictions versuslarge information sets in forecasting the yield curve, Favero et al. (2012)investigate the forecasting performance of the DNS, the ATSM with asmall number of macroeconomic variables and the ATSM with a largeset of macroeconomic variables. Following the literature, instead ofusing all ofmacroeconomic variables individually, they extract commonfactors. They find that macro factors are very useful in forecasting themedium and the long rates and the financial factors are very useful inforecasting the short rates. They also show that themodels withmacro-economic variables have superior forecasting performance than thoseof the random walk for most of the cases considered.

In this study, we investigate forecasting performance of the DNS,the ATSM VAR and principal component (PC) models in Turkey. Byincorporating a set of macroeconomic variables, we analyze the role ofmacroeconomic variables in forecasting the yield curve. Since the Turkisheconomy has experienced a monetary policy change in 2002 accompa-nied by a political change around 2002, we regard this date as a potentialdate of a structural break. To take the structural break into account wedivide the samples into pre-2002 and post-2002 periods. In our case,the change in monetary policy is associated with the implementationof an Inflation Targeting (IT) regime.

The rest of the paper consists of six parts. The first part describesthe data set. The second part provides a general framework for fore-cast. The third part presents models and estimation techniques. Thefourth part provides forecasting procedure. The fifth part presentsthe empirical findings and the last part concludes.

2. Data

The data set consists of monthly observation of annual interestrates over the period 1993:M1–2011:M8. To construct the yields,we use Treasury bond rates with maturities of 1, 2, 3, 4, 6 and12 months. All the yields are continuously compounded and then-month maturity yield is denoted by yt(n). These data are obtainedfrom the Istanbul Stock Exchange database on a daily basis1 andmonthly averages are used in the estimation. It is not possible tofind the interest rates for longer maturities in the Turkish economy,especially in the 90s mainly because of the lack of deep financialmarket, high levels of uncertainty and political instability.2

We use a number of macroeconomic variables namely inflationdenoted by πt, output gap denoted by gapt, exchange rate denoted

1 The interest rate data has been obtained by Riskturk (www.riskturk.com). Inconstructing the yield curve official bond market data has been collected from IstanbulStock Exchange. Since the Turkish Fixed Income Bill and Bonds are traded in an officialexchange (more information can be found at http://www.ise.org) a reliable official da-ta exists and the market is rather liquid for an emerging market. Once the official datais obtained from the ISE, the spot yields are solved. More details can be found in http://www.riskturk.com.

2 During the 1993–2002 period Turkey experienced three financial crises and a greatearthquake. During 1989–1993 CBRT mostly did not sterilize the capital inflow howev-er in the 1995–1999 period CBRT chose to sterilize inventory policy. On the other hand,over the 2000–2001 period fixed exchange rate regime is used. Turkey had 11 differentgovernments during the period 1990 to 2000. For an overview of the Turkish economyduring this period, see Telatar et al. (2003) and, Kaya and Yazgan (2011).

by et, and policy rate denoted by prt. Inflation rate is calculated asπt = (log CPIt − log CPIt − 12) where CPI denotes Consumer PriceIndex. The CPI series are obtained from the International FinancialStatistics of the IMF and seasonally adjusted. Output gap is calculatedby using seasonally adjusted Industrial Production Index. We use themethod of Hördahl et al. (2006) to measure output gap in which ratherthan detrending full samplewe generate a series recursively. In this set-ting, to obtain the value of output at time t, we fit the Hodrick–Prescotttrend to the original series up to that time. This process was repeateduntil the end of the period. By adopting this, we ensure that our mea-sure of output gap at time t does not rely on unavailable informationat that point.

For exchange rate data, we use the Turkish Lira effective exchangerate against the US Dollar. For policy rate, we use the overnight inter-est rate of the Central Bank of Turkey (CBT).

To investigate the time series properties of these variables, we em-ploy three different unit root tests to obtain possibly robust results.We find that all the series contain a unit root in their levels.3 Incontrast, their first differences appear to be stationary. The onlyexception is the inflation where only the unit root tests taking intoaccount structural breaks indicate stationarity. As is well known,Perron (1989, 1997) asserts that a stationary series can be spuriouslydetected as non-stationary in the presence of breaks.

Table 1 shows the descriptive statistics of the yields. The last threecolumns contain the sample correlations at displacements of 1, 12and 24 months and they suggest that the long-run interest rates aremore persistent than the short-run interest rates. Fig. 1 plots the low-est (1 month), the highest (12 months) maturity interest rates andinflation. The short and long rates move very closely and both thelevel and the variation of interest rates have decreased after 2002.The decrease in the yields appears to be very related to the level ofinflation in Turkey.

In the literature, it is well documented that the relationship betweenthe yield curve and macroeconomic variables is unstable and the mainsource of instability is regarded as the monetary policy (see for exam-ple, Bansal and Zhou, 2002; Dai et al., 2003; Kozicki and Tinsley, 2001;Stock and Watson, 2003). As discussed in Elliott and Timmermann(2008) and Clements and Hendry (2006), among others, instability isone of the key determinants of forecasting performance.

In Turkey there is a monetary policy shift in 2002 in which the infla-tion targeting is started. Before 2002, monetary policy incorporated thepractice of fixed or managed exchange rate regimes. After the deep fi-nancial crisis of February 2001, a structural transformation process in-volving not only the transition to the inflation targeting but also theintroduction of the floating exchange rate regime coupled with thenew central bank law, and structural reforms has been implemented(Basci et al., 2008). Accordingly, in many studies 2002 is regarded as aturning point for the Turkish economy (see for example, Civcir andAkçaglayan, 2010; Kaya and Yazgan, 2011; Tastan, in press).

To take the structural break into account, we estimate any givenmodel in each period. Thus we divide the sample period as1993:01–2001:12 (pre-2002) and 2002:01–2011:08 (post-2002)and conduct forecasting exercises for these periods also.

3. A general framework for forecasting

Favero et al. (2012) propose a general state space representationto evaluate the forecasting performance of empirical models of theyield curve and the effects of incorporating additional information

3 They include 3 different ADF tests, KPSS test and Phillips–Perron test. The ADF-WS(Park and Fuller, 1995) and the ADF-GLS test (Elliott et al., 1996) are used in additionto the standard ADF test. To control structural breaks, we used Perron's (1989, 1997)unit root tests. To save space, we do not report these results; however, they are avail-able upon request.

0.0

0.4

0.8

1.2

1.6

2.0

1994 1996 1998 2000 2002 2004 2006 2008 2010

y(1)y(12)inflation

Fig. 1. y(1), y(12) and inflation.

Table 1Descriptive statistics.

Mean Maximum Minimum Std. dev. p1 p12 p24

TR1 0.590 6.979 0.060 0.653 0.765 0.387 0.345TR2 0.605 3.433 0.059 0.545 0.932 0.558 0.501TR3 0.620 3.192 0.060 0.540 0.951 0.590 0.524TR4 0.631 3.123 0.062 0.546 0.957 0.599 0.527TR6 0.639 2.926 0.065 0.538 0.965 0.631 0.543TR9 0.629 2.268 0.065 0.500 0.973 0.695 0.590TR12 0.619 2.212 0.069 0.490 0.971 0.696 0.592

Note: The last three columns contain sample autocorrelations at displacements of 1, 12and 24 months. The sample period is 1993:01–2011:08.

3H. Kaya / Economic Modelling 33 (2013) 1–7

to the model. The dynamics of the term structure can be described byfollowing the state space framework;

yt nð Þ ¼ An þ B′nXt þ εt nð Þ εt nð Þ∼i:i:d: N 0;σ2I

� �ð1Þ

Xt ¼ μ þΦXt−1 þ υt υt nð Þ∼i:i:d: N 0;Ωð Þ ð2Þ

where yt(n) is the yield to maturity at time t of a bond maturing attime t + n. The variables in Xt can be endogenous or exogenous, ob-servable or latent. Eq. (1) is the measurement equation in which theterm structure of interest rate is assumed to be determined by a setof state variables Xt. Eq. (2) is the state equation in which the statevariables are assumed to follow a VAR(1) process. This unified frame-work enables an analysis of forecasting performance of different yieldcurve models by incorporating different specifications of informationset.

4. Models and estimation methods

In this part we introduce three types of specifications and theirestimation techniques. The employed specifications for forecastinganalysis are as follows: the DNS, the ATSM VAR, and the principalcomponent analysis.4

4.1. Dynamic Nelson–Siegel Model

Among practitioners Nelson and Siegel's (1987) representation ofthe yield curve is very popular. Nelson and Siegel's representation is:

yt nð Þ ¼ β1 þ β21−e−λtn

λtn

!þ β3

1−e−λtn

λtn−e−λtn

!ð3Þ

where β1, β2, β3 and λt are parameters. Diebold and Li (2006) showthat the Nelson–Siegel yield curve representation is a dynamic latentthree-factor model in which β1t, β2t and β3t are time varying level,slope and curvature factors. The Dynamic Nelson–Siegel Model (DNS)is;

yt nð Þ ¼ β1t þ β2t1−e−λtn

λtn

!þ β3t

1−e−λtn

λtn−e−λtn

!ð4Þ

where the parameter λt governs the exponential decay rate. Smallvalues of λt produce slow decay and large values of λt produce fast

4 As it is clearly seen in Fig. 1, the yield curve in Turkey is inverted in 1994, 2000 and2001 which are the crises years. While the DNS has the ability to replicate a variety ofshapes through time depending on the variation in the time varying factors, the no-arbitrate models do not perform well empirically. For a detailed discussion on themodels' ability to replicate a variety of shapes of the yield curve see Diebold and Li(2006), Duffee (2002), Gasha et al. (2010), Litterman and Scheinkman (1991) andPiazzesi (2009).

decay and small and large values better fit the curve at the short endand at the long end respectively. Additionally, λt determines whereβ3t reaches its maximum. To represent DNS in the unified frameworkwe define An = 0, and

B′n ¼ 1;

1−e−λtn

λt

!;

1−e−λtn

λt−e−λtn

!" #

The state equation Xt = βt is assumed to follow a VAR(1) process;

βt ¼ μ þΦβt−1 þ υt ð5Þ

where βt = [β1t,β2t,β3t] is the vector of three DNS factors.We estimate the parameters of β1t, β2t and β3t by using Diebold

and Li's (2006) two stage estimation method. First we fix λt andthen use OLS. We can find an appropriate value for λt, if we considerthat λt determines the maturity at which the curvature factor namelyβ3t reaches its maximum. In the literature, two or three years is com-monly used for that purpose. Nonetheless, in our study the longestmaturity is 12 months. Taking the maturities into considerationthree or four months can be properly used, and we use the averageof these and pick 3.5 months. We find that the value that maximizesthe loadings on β3t at maturity 3.5 (i.e. n = 3.5) months is 0.4483.Using n = 3.5 and λt = 0.4483 we estimate β1t, β2t, and β3t by OLS.

4.2. ATSM VAR specification

The assumption of no-arbitrage is very common in most of theempirical analyses of bond pricing and the yield curve modeling.The canonical affine term structure models under the no-arbitrageassumption contain three basic equations; i—short rate equation tobe affine function of the state variables (constant plus linear term),ii—transition equation for the state vector relevant for pricing bondand, iii—price of risk to be a linear function of the state of the econo-my (Rudebusch and Wu, 2003).

We assume that the short rate, rt, is an affine function of the statevariables (Ang and Piazzesi, 2003; Ang et al., 2006; Hördahl et al.,2006; Rudebusch and Wu, 2003);

rt ¼ δ0 þ δ′1Xt ð6Þ

Assume that the state variables of Xt + 1 follow a VAR(1) process

Xtþ1 ¼ μ þΦXt þ εtþ1 ð7Þ

Following Constantinides (1992), Dai and Singleton (2000), Duffee(2002) and Ang and Piazzesi (2003), among others, we define the

4 H. Kaya / Economic Modelling 33 (2013) 1–7

time varying market price of risk Λt as a linear function of the statevariables;

Λ t ¼ Λ0 þ Λ1Xt ð8Þ

Following the literature we define time series properties of thepricing kernel5 M(t) as;

Mtþ1 ¼ exp −rt−12Λ ′

tΩΛ t−Λ ′tεtþ1

� �ð9Þ

In an arbitrage free market the return of an asset satisfies;

Et Mtþ1Rntþ1

� � ¼ 1 whereRnt representsgrossreturnwhichisRn

t

¼ Pnt

Pnt−1

;wherePnt is thepriceof ann

� periodzerocouponbond:

So we have

Pnþ1t ¼ E Mtþ1P

ntþ1

� � ð10Þ

If we assume that the bond prices are an exponential affine func-tion of the state variable then

Pnt ¼ exp An þ B′

nXt

� �ð11Þ

When the equation system is solved, one can easily generate thatthe continuously compounded yield yt(n) on an n-period zero couponbond is an affine function of the state variables;

yt nð Þ ¼ − logPnt

n¼ An þ B′

nX ð12Þ

where An ¼ −Ann and Bn ¼ −Bn

n and

Anþ1 ¼ A1 þ An þ B′nμ−B′

nΩΛ0 þ12B′

nΩBn ð13Þ

B′nþ1 ¼ B′

1 þ B′nΦ−B′

nΩΛ1 ð14Þ

The restrictions imply that, given the coefficients of short rateequation (A1, B1), all the other coefficients for the longer maturityyields are determined by the state equation and the risk pricing equa-tion. These restrictions make the yield equation consistent with eachother both in the cross-section and in the time series. On the otherhand, these restrictions reduce the number of variable needed todescribe the yield curve.

We assume that the state variables consist of unobserved andobserved factors. Following Chen and Scott (1993), the unobservedfactors are extracted by inverting the measurement equation. Weassume that there are K factors in the state equation: K1 areunobserved and K2 are observed factors. We assume that K2 yieldsare measured without error and K1 yields are measured with error.After solving the latent factors from the yields, the correspondinglikelihood function is developed and the parameters are estimated(for the likelihood function, see Ang and Piazzesi, 2003).

Since Dai and Singleton (2000), analyzing affine term structuremodels, show that the yield curve movements can be reduced tothree factors. In this setup we use three Chen–Scott unobserved

5 Pricing kernel has an economic interpretation in which it can be derived from thefirst order conditions of an intertemporal utility maximization problem. Given that the

utility function of an agent is U Ctð Þ ¼XTt¼0

βtE0 u Ctð Þ½ �, then the pricing kernel can be

characterized as Mtþ1 ¼ βu′ Ctþ1ð Þu′ Ctð Þ .

factors, denoted by CSt = [CS1, CS2, CS3], as the state variables. Wedefine Xt = CSt.

In the estimation, we allow time varying risk price and assumethat λ1 is diagonal. We assume that the factors have zero mean andthe variance covariance matrix Ω is diagonal which are the mostgenerally identified representation (Dai and Singleton, 2000; Favero etal., 2012). The assumption of diagonal λ1 and Ω implies that the priceof risk is independent. In the short rate equation, yt 1ð Þ ¼ −A1−B1X,we restrict−A1 to be the historical mean of the short rate.We usemax-imum likelihood estimation. Assuming that 1, 4 and 12 month yieldsare measured without error, we invert the measurement equation andcalculate the likelihood function.

4.3. Principal component analysis

For the third specification,we performprincipal component analysiswhich enablesmodeling the variance structure of all the yields by usinglinear combinations of a small number of unobservable variables calledthe factors. Principal component analysis effectively decomposes theyield covariancematrix as LVL′, where the diagonal elements of V are ei-genvalues and columns of L are corresponding eigenvectors. Since wehave seven yields,we have seven eigenvalues. Denoting the eigenvaluesas ζi, i = 1,2,…7, associated eigenvectors as qi, i = 1,2,…7 and principalcomponents as PCi, then the principal components are defined byPCit = q′ityt(n). By following Diebold and Li (2006) and Alper et al.(2007) we use the first three principal components which are calculat-ed by using the largest three eigenvalues.

Hence, in this setup we allow that yt(n) follows a three factormodel;

y nð Þt ¼ φPCt þ εtt ð15Þ

where φ is the matrix of factor loadings in which each element givesinformation about the effects of a unit change in a factor on observedyields, PCt = [PC1,t, PC2,t, PC3,t] is the vector of the first three principalcomponents with diagonal covariance matrix and εt measurementerror with E(εt) = 0.

When we represent this setup in the unified state space frame-work then;

An ¼ 0;B′n ¼ C and Xt ¼ PCt

5. Yield curve forecasting

In forecast analysis we investigate forecasts at different horizons. Inmulti-period ahead forecast, we choose to direct forecasting whichmight have advantageous over one period iterated forecast when themodel is misspecified.6

X tþhjt ¼ c þ ϒX t ð16Þ

where c and ϒ are obtained by regressing X t on intercept and X t−h.Yield forecasts based on the DNS are calculated as follows;

⌢ytþhjt τð Þ ¼ ⌢β1;tþhjt þ ⌢β2;tþhjt1−eλτ

λτ

!þ ⌢β3;tþhjt

1−eλτ

λτ −eλτ !

ð17Þ

where

⌢βtþh t¼aþΓ h

⌢βt

�� ð18Þ

6 We also investigate one step ahead forecasting by iterated projections, X tþhjt ¼Xhi¼1

Φi−1 μ þΦhX t , but direct forecasting shows superior performance.

Table 2RMSFE ratio with respect to random walk: entire period.

N Yield-only[AR(1)]

Yield-only[VAR(1)]

+macro:{πt,gapt,prt}

+macro:{πt, gapt,Δet}

NS CS PC NS CS PC NS CS PC NS CS PC

h = 11 1.54 3.73 2.01 3.40 4.15 3.42 4.09 4.16 4.09 6.41 6.59 6.512 3.11 1.72 1.61 2.89 2.08 2.96 3.73 5.04 3.50 5.37 4.85 4.963 3.75 1.48 2.31 2.66 3.57 2.66 3.32 3.25 3.21 4.55 4.90 4.324 3.92 2.13 2.51 2.57 3.06 2.55 2.95 2.90 3.03 3.98 4.10 4.096 3.52 3.20 2.97 2.32 3.67 2.38 2.21 2.57 2.38 3.04 4.00 3.399 2.74 3.49 3.76 1.87 3.67 2.12 1.46 2.60 1.45 2.14 3.68 2.2912 2.38 1.99 3.32 1.69 1.92 1.53 1.25 1.26 1.18 1.89 1.86 1.60

h = 31 4.16 1.67 1.14 1.77 2.02 1.77 1.71 1.78 1.72 2.89 2.96 2.942 5.03 1.08 1.19 1.66 1.22 1.64 1.53 1.92 1.43 2.41 2.01 2.243 5.22 1.15 1.39 1.54 1.81 1.50 1.32 1.37 1.27 1.99 2.17 1.904 5.46 1.37 1.48 1.51 1.65 1.49 1.22 1.23 1.25 1.80 1.86 1.856 5.28 1.80 1.68 1.43 1.94 1.46 1.02 1.31 1.08 1.49 1.96 1.659 4.62 1.96 2.04 1.29 2.00 1.39 0.88 1.47 0.95 1.24 1.94 1.3312 4.30 1.40 1.91 1.26 1.32 1.18 0.92 0.93 0.84 1.23 1.21 1.08

h = 61 2.45 1.12 0.96 1.34 1.45 1.35 0.95 1.00 0.95 1.77 1.82 1.802 2.89 0.96 1.08 1.29 1.03 1.29 0.89 0.96 0.87 1.51 1.18 1.443 3.06 1.09 1.17 1.24 1.37 1.23 0.85 0.90 0.83 1.33 1.44 1.294 3.18 1.20 1.22 1.24 1.30 1.23 0.83 0.85 0.83 1.25 1.28 1.276 3.09 1.42 1.31 1.19 1.45 1.21 0.81 1.01 0.82 1.12 1.39 1.199 2.84 1.53 1.52 1.13 1.51 1.19 0.82 1.18 0.89 1.05 1.46 1.1212 2.69 1.22 1.44 1.11 1.14 1.07 0.88 0.89 0.82 1.06 1.06 0.98

h = 91 1.76 1.02 0.97 1.18 1.23 1.19 0.89 0.91 0.90 1.38 1.40 1.392 2.03 0.93 1.04 1.15 0.93 1.16 0.86 0.84 0.86 1.23 1.00 1.203 2.14 1.07 1.08 1.12 1.19 1.13 0.85 0.88 0.84 1.14 1.20 1.134 2.23 1.14 1.11 1.13 1.16 1.13 0.86 0.86 0.86 1.11 1.12 1.126 2.20 1.29 1.17 1.11 1.28 1.12 0.85 0.99 0.86 1.05 1.23 1.099 2.05 1.38 1.31 1.07 1.33 1.12 0.87 1.11 0.93 1.01 1.29 1.0612 1.95 1.15 1.23 1.05 1.06 1.03 0.91 0.92 0.87 1.02 1.02 0.97

h = 121 1.37 0.93 0.97 1.11 1.13 1.12 0.96 0.96 0.96 1.24 1.24 1.242 1.57 0.90 1.03 1.10 0.91 1.12 0.94 0.88 0.94 1.18 1.03 1.183 1.67 1.05 1.06 1.09 1.14 1.10 0.92 0.95 0.92 1.14 1.17 1.144 1.74 1.10 1.08 1.10 1.11 1.10 0.93 0.93 0.93 1.12 1.13 1.136 1.74 1.24 1.13 1.08 1.22 1.09 0.92 1.03 0.93 1.07 1.20 1.099 1.65 1.32 1.23 1.05 1.26 1.09 0.92 1.12 0.96 1.03 1.24 1.0712 1.59 1.13 1.17 1.04 1.04 1.02 0.94 0.94 0.91 1.02 1.02 0.99

Notes: The first and second columns show the RMSFE ratio based on that the yieldfactors are AR(1) and VAR(1) respectively. The third column shows RMSFE ratiobased on that the state vector contains the yield factors and macro information of infla-tion, output gap and policy rate. The last column shows the RMSFE ratio based on thatthe state vector contains the yield factors and macro information of inflation, outputgap and change in exchange rate. The emboldened entries indicate that the model pro-duces better forecasts than the random walk.

5H. Kaya / Economic Modelling 33 (2013) 1–7

a and Γ h are estimated by regressing⌢βt on intercept and⌢βt−h. First weextract the DNS factors from the yields, using the method we describeearlier, and holding the loadings of the yields on the DNS factors inthe measurement equation fixed, forecasted yields are generated byusing the forecasted DNS factors. Forecasts in the third specificationare obtained by the same procedure.

In the ATSM VAR model, first the loadings of the yields on the CSfactors in the measurement equation are estimated by using Eq. (7),and then using Eq. (16) forecasts of the CS factors are calculated.Using the previously estimated loadings, we obtain forecasted yields.

Diebold and Li (2006) argue that it might be expected that the ARforecasts tend to be superior to the VAR forecast. Thereby, in additionto the forecasts based on VAR(1) factors, we also produce forecastsbased on the assumption that the factors are univariate AR(1).

To see whether incorporating macroeconomic variables improvesthe forecasting performance, as in Favero et al. (2012), we modeledthe yield factors together with the macro factors as a VAR(1). Thestate vector in this case is Xt = [ ftzt]′ where ft contains the yieldfactors (DNS, CS and PC) and zt contains the macroeconomic vari-ables. For the first and third specifications, the NS factors and the PCfactors are extracted from the yields as before. We assume that,following Favero et al. (2012) and Diebold et al. (2006), the factorloadings of the yields on zt in the measurement equation is zero. Forthe no-arbitrage specification, we do not impose any restriction onthe factor loadings of the yields on zt.

In the literature, measures for inflation and real activities are com-monly used for macroeconomic information. However, in an emerg-ing market like Turkey, exchange rate plays a crucial role both inthe financial markets and macroeconomy (Berument and Gunay,2003; Celasun et al., 2004; Diboğlu and Kibritçioğlu, 2004; Leighand Rossi, 2002). Therefore, we use exchange rate as macroeconomicinformation.

In the forecast experiment, first we use a set of three macroeco-nomic variables; the inflation, the output gap and the policy rateand then replacing the policy rate with the exchange rate we useanother set of information. By doing this, we aim to see the effectsof exchange rate in forecasting the yield curve in Turkey.

As a benchmark model we produce random walk forecasts where;

y nð Þtþhjt ¼ y nð Þ ð20Þ

The forecast is always “no change”.

6. Empirical results

To measure the forecasting performance, we use ratio of root meansquare forecast errors (RMSFE) of each model to the RMSE of the ran-domwalk. We use rolling window estimation method in which holdingthe sample size fixed wemove the sample forward one observation at atime. For the entire period and the post-2002 sub-sample, the forecastedperiod is 2006:09–2011:08. For thepre-2002 sub-sample, the forecastedperiod is 1998:01–2001:12.We consider a range of forecasting horizons,h: 1 month, 3 months, 6 months, 9 months and 12 months. Thus, forthe 1-month-ahead forecasting horizon, we end up with a total of 60forecasts; and for the 3, 6, 9 and 12-month ahead forecasting horizons,we end up with a total of 58, 55, 52 and 49 forecasts respectively.

We report comparisons of the forecasting results from differentmodel specifications in Tables 2–4. Table 2 shows the results for the en-tire period, Table 3 shows the results for the pre-2002 sub-period andTable 4 shows the forecasting results for the post-2002 sub-period.Since the measure of forecasting performance is the ratio of RMSFE ofeach model to the RMSFE of the random walk, a ratio that is less thanone indicates that the corresponding model produces better forecaststhan the random walk. In the tables, the first and second columnsshow the results of the yield-only models in which the yield factors aremodeled as AR(1) and as VAR(1) respectively. The third column shows

the results of themodels inwhich the state vector contains the yield fac-tors andmacroeconomic information of the inflation, the output gap andthe policy rate. The last column shows the results ofmodels inwhich thestate vector contains the yield factors and macroeconomic informationof the inflation, the output gap and the change in the exchange rate.

The results for the entire period suggest that the forecasts of theyield-only model cannot beat those of the random walk, in general.The results show that the DNS and the ATSM VAR models with theVAR(1) factors produce better forecasts than with the AR(1) factors.For the PC model, the AR(1) specification produces better forecaststhan the VAR(1). Incorporating macroeconomic information of theinflation, the output gap and the policy rate significantly improvethe forecasting performance of the models and, for h > 3 the modelscan beat the random walk. However, replacing the policy rate withthe change in the exchange rate deteriorates the forecasts.

For the pre-2002 sub-period, the yield-only models can beat therandomwalk in most of the cases considered. In terms of the forecast-ing performance of the yield-only specification, the ATSM VAR is thebest. In this period also the DNS and the ATSM VAR with the AR(1)produce better forecasts than those with the VAR(1). When we

Table 3RMSFE ratio with respect to random walk: pre-2002 period.

N Yield-only[AR(1)]

Yield-only[VAR(1)]

+macro:{πt,gapt,prt}

+macro:{πt, gapt,Δet}

NS CS PC NS CS PC NS CS PC NS CS PC

h = 11 1.22 0.98 1.00 1.09 1.15 1.11 1.22 0.98 1.00 1.14 1.14 1.202 1.30 0.95 0.94 1.02 1.00 0.97 1.30 0.95 0.94 1.03 1.16 0.983 1.36 1.05 0.99 1.03 1.03 1.01 1.36 1.05 0.99 1.07 1.13 1.044 1.42 1.14 1.03 1.05 1.07 1.06 1.42 1.14 1.03 1.11 1.13 1.116 1.55 1.36 1.07 1.07 1.17 1.10 1.55 1.36 1.07 1.18 1.19 1.209 1.69 1.54 1.08 1.13 1.34 1.12 1.69 1.54 1.08 1.26 1.31 1.2612 1.44 1.19 0.96 1.01 1.08 0.99 1.44 1.19 0.96 1.11 1.19 1.10

h = 31 1.04 0.94 1.00 1.03 1.07 1.04 1.20 1.27 1.21 0.97 0.95 1.012 0.95 0.93 0.95 0.95 1.03 0.95 1.04 1.16 1.01 0.94 1.08 0.943 0.97 0.93 0.97 0.97 0.99 0.97 1.05 1.12 1.04 0.98 1.01 0.984 1.00 0.97 0.99 1.00 1.00 1.00 1.10 1.15 1.08 1.01 1.00 1.006 1.05 1.05 1.02 1.04 1.04 1.03 1.17 1.22 1.15 1.05 1.00 1.049 1.10 1.11 0.99 1.01 1.05 1.00 1.19 1.28 1.16 1.03 1.00 1.0312 1.05 1.02 0.94 0.96 0.98 0.96 1.14 1.24 1.12 0.98 1.00 0.99

h = 61 0.98 0.91 1.00 1.01 1.05 1.02 1.15 1.19 1.17 0.85 0.86 0.872 0.95 0.91 0.96 0.96 0.99 0.94 1.05 1.09 1.02 0.89 0.97 0.883 0.95 0.92 0.98 0.96 0.99 0.96 1.03 1.08 1.02 0.92 0.96 0.924 0.96 0.94 1.00 0.97 0.99 0.98 1.03 1.07 1.04 0.94 0.95 0.956 1.00 0.99 1.02 1.00 1.02 1.02 1.06 1.11 1.09 0.96 0.95 0.989 1.04 1.03 1.00 1.02 1.05 1.02 1.10 1.16 1.09 0.98 0.98 0.9812 1.02 0.98 0.96 0.99 1.01 0.98 1.07 1.13 1.05 0.94 0.96 0.94

h = 91 0.96 0.90 1.01 1.02 1.05 1.03 1.12 1.15 1.15 0.87 0.88 0.882 0.94 0.91 0.98 0.98 1.02 0.96 1.03 1.07 1.00 0.89 0.97 0.893 0.94 0.92 1.00 0.98 1.01 0.98 1.02 1.05 1.01 0.93 0.97 0.944 0.94 0.92 1.01 0.99 1.00 1.00 1.01 1.04 1.02 0.94 0.96 0.956 0.97 0.96 1.03 1.01 1.03 1.04 1.04 1.07 1.06 0.98 0.98 0.989 0.99 0.99 1.00 1.02 1.04 1.02 1.05 1.10 1.05 0.97 0.98 0.9712 1.00 0.97 0.98 1.02 1.03 1.01 1.06 1.11 1.05 0.95 0.98 0.96

h = 121 0.91 0.87 1.00 1.00 1.00 0.99 1.11 1.09 1.13 0.99 0.98 0.992 0.89 0.90 0.98 0.97 1.02 0.96 1.04 1.08 1.03 0.96 1.03 0.953 0.90 0.90 1.01 0.99 1.01 0.99 1.05 1.07 1.05 0.98 1.02 0.994 0.90 0.90 1.00 0.99 0.99 0.99 1.04 1.04 1.05 0.99 1.00 0.996 0.92 0.92 1.01 1.00 0.99 1.01 1.05 1.04 1.06 1.01 1.00 1.019 0.92 0.94 0.98 1.00 1.00 0.99 1.05 1.05 1.04 1.01 1.01 1.0112 0.91 0.93 0.98 0.99 1.01 0.99 1.05 1.06 1.05 1.00 1.02 1.01

Notes: The first and second columns show the RMSFE ratio based on that the yieldfactors are AR(1) and VAR(1) respectively. The third column shows RMSFE ratiobased on that the state vector contains the yield factors and macro information of infla-tion, output gap and policy rate. The last column shows the RMSFE ratio based on thatthe state vector contains the yield factors and macro information of inflation, outputgap and change in exchange rate. The emboldened entries indicate that the model pro-duces better forecasts than the random walk.

Table 4RMSFE ratio with respect to random walk: the post-2002.

n Yield-only[AR(1)]

Yield-only[VAR(1)]

+ macro:{πt,gapt,prt}

+macro:{πt, gapt,Δet}

NS CS PC NS CS PC NS CS PC NS CS PC

h = 11 1.37 1.61 1.07 1.06 1.09 1.05 0.93 0.96 0.93 1.04 1.04 1.032 1.32 1.46 1.02 1.04 1.03 1.04 0.98 0.98 0.97 0.94 0.95 0.953 1.33 1.41 1.02 1.07 1.03 1.07 1.07 1.03 1.05 0.94 0.91 0.934 1.37 1.41 1.04 1.12 1.09 1.11 1.17 1.12 1.17 0.99 0.97 1.016 1.31 1.31 1.02 1.10 1.14 1.11 1.14 1.16 1.16 0.99 1.03 1.019 1.22 1.24 0.99 1.06 1.11 1.09 1.15 1.21 1.17 1.04 1.09 1.0612 1.19 1.17 0.95 1.06 1.05 1.03 1.21 1.21 1.18 1.09 1.08 1.06

h = 31 1.10 1.13 1.00 0.99 1.00 1.00 0.89 0.87 0.89 0.89 0.87 0.892 1.11 1.12 0.99 1.01 1.00 1.01 0.91 0.88 0.91 0.90 0.88 0.903 1.09 1.09 0.98 1.01 1.00 1.01 0.93 0.89 0.92 0.91 0.89 0.904 1.12 1.12 0.99 1.04 1.03 1.04 0.97 0.94 0.96 0.94 0.93 0.946 1.12 1.12 1.00 1.05 1.07 1.06 0.99 1.00 1.00 0.97 0.99 0.989 1.08 1.09 0.98 1.02 1.05 1.04 0.98 1.01 1.00 0.97 0.99 0.9912 1.08 1.06 0.95 1.02 1.02 1.00 1.01 1.01 0.99 1.00 0.98 0.98

h = 61 1.04 1.03 0.99 0.98 0.99 0.99 0.92 0.91 0.93 0.91 0.90 0.912 1.05 1.02 0.98 1.00 0.98 0.99 0.93 0.89 0.93 0.92 0.90 0.923 1.04 1.02 0.98 1.00 0.99 1.00 0.93 0.90 0.94 0.93 0.92 0.934 1.06 1.05 0.99 1.02 1.01 1.02 0.96 0.94 0.95 0.96 0.95 0.956 1.06 1.06 1.00 1.03 1.04 1.03 0.97 0.98 0.98 0.97 0.98 0.989 1.04 1.06 0.99 1.02 1.03 1.03 0.98 1.00 0.99 0.98 1.00 0.9912 1.04 1.03 0.96 1.01 1.01 1.00 0.98 0.98 0.97 0.99 0.98 0.97

h = 91 1.03 1.03 0.99 0.99 0.99 1.00 0.97 0.95 0.97 0.95 0.95 0.952 1.03 1.02 0.98 0.99 0.98 0.99 0.96 0.93 0.96 0.95 0.94 0.953 1.03 1.02 0.98 1.00 0.98 1.00 0.96 0.93 0.96 0.96 0.95 0.964 1.04 1.04 0.99 1.01 1.01 1.01 0.98 0.96 0.98 0.98 0.98 0.986 1.04 1.05 1.00 1.02 1.03 1.02 0.99 0.99 0.99 0.98 1.00 0.999 1.03 1.05 0.99 1.00 1.02 1.01 0.98 1.00 0.99 0.97 1.00 0.9812 1.02 1.02 0.96 1.00 1.00 0.99 0.98 0.97 0.97 0.97 0.97 0.96

h = 121 1.02 1.01 0.99 0.99 0.99 0.99 0.98 0.97 0.99 0.96 0.96 0.962 1.02 1.00 0.98 0.99 0.98 0.99 0.98 0.95 0.98 0.96 0.95 0.963 1.02 1.00 0.99 0.99 0.98 0.99 0.97 0.95 0.98 0.97 0.96 0.974 1.03 1.02 0.99 1.01 1.00 1.00 0.99 0.97 0.98 0.98 0.98 0.986 1.03 1.04 1.00 1.01 1.02 1.01 0.99 1.00 1.00 0.99 1.00 0.999 1.02 1.04 0.99 1.00 1.02 1.01 0.99 1.00 1.00 0.98 1.00 0.9912 1.02 1.01 0.97 1.00 1.00 0.99 0.99 0.98 0.98 0.98 0.98 0.97

Notes: The first and second columns show the RMSFE ratio based on that the yieldfactors are AR(1) and VAR(1) respectively. The third column shows RMSFE ratiobased on that the state vector contains the yield factors and macro information of infla-tion, output gap and policy rate. The last column shows the RMSFE ratio based on thatthe state vector contains the yield factors and macro information of inflation, outputgap and change in exchange rate. The emboldened entries indicate that the model pro-duces better forecasts than the random walk.

6 H. Kaya / Economic Modelling 33 (2013) 1–7

incorporate the macroeconomic variables the results show that,especially for the short maturities, the models including the firstinformation set produce better forecasts than the yield-only modelsfor h = 6 and h = 9. However, incorporating the second informationset worsens the forecasting performance of the models. These resultssuggest that the exchange rate plays an important role in the bondmarket in the pre-2002 period. Considering the characteristics ofthis period, which are the high level of inflation associated withuncertainty, and highly dollarized economy (see Basci et al., 2008),these findings are not surprising.

For the post-2002 sub-period, the yield-only PC model with anAR(1) specification produces superior forecasts than the DNS andATSM VAR models. For h ≥ 3, forecasts of the yield-only PC modelare better than those of the random walk. For the short maturitiesand longer forecast horizons, the DNS and the ATSM VAR modelsalso produce better forecasts than the random walk. Incorporatingmacroeconomic information increases the forecasting performanceof the models and, for h > 1 and for almost all the maturities themodels can beat the random walk. In this period, the results of boththe sets of macroeconomic information are similar.

7. Conclusion

In this study we investigate the yield curve forecasting performanceof three specifications namely Dynamic Nelson–Siegel Model (DNS),no-arbitrage affine term structure VAR (ATSM) model and principalcomponent (PC) analysis in Turkey. To take into account the structuralbreak, we divide our sample as pre-2002 and post-2000 period. Forthe entire period and two sub-periods, firstly we investigate the fore-casts of the yield-only models, i.e. we use only extracted yield factorsfor forecasting, and then we incorporate two sets of macroeconomicinformation; the first set contains inflation rate, output gap and policyrate and the second set contains inflation, output gap and exchangerate. The out of sample forecasting experiment shows that the forecast-ing performances of the models are time varying. In the entire period,the yield-only models cannot beat the random walk but in thepre-2002 sub-period the yield-only models produce superior forecaststhan the random walk. For the post-2002 sub-period, the yield-onlyPC model can beat the random walk for medium and long forecastinghorizons. We find that, the macro factors are very useful in forecastingthe yield curve. For the entire period, the first macroeconomic

7H. Kaya / Economic Modelling 33 (2013) 1–7

information set significantly improves the forecasting performance ofthe models. For the pre-2002 period, replacing the policy rate withthe exchange rate produces better forecasts. However, for the post-2002 period both the macroeconomic information sets rate producesimilar results.

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