financial time series
DESCRIPTION
Financial Time Series. CS3. Financial Time Series. Outline. Discrete Time Series Analysis Continuous Time Series Analysis. Discrete Time Series Analysis. Comes from the same distribution. Auto-regressive model. ~. Moving Average Model. MA(1). Weighted Average of Shocks. Why?. ARMA. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/1.jpg)
Financial Time Series
CS3
![Page 2: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/2.jpg)
Financial Time Series
![Page 3: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/3.jpg)
![Page 4: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/4.jpg)
Outline
• Discrete Time Series Analysis• Continuous Time Series Analysis
![Page 5: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/5.jpg)
Discrete Time Series Analysis
![Page 6: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/6.jpg)
Comes from the same distribution
![Page 7: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/7.jpg)
Auto-regressive model
~
![Page 8: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/8.jpg)
Moving Average Model
Weighted Average of Shocks
Why?
MA(1)
![Page 9: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/9.jpg)
ARMA
• Combination of AR and MA
![Page 10: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/10.jpg)
Learning the Parameters
• Easy !!! just apply normal regression analysis techniques
• However, there are sophisticated method like Partial Auto-correlation (PACF).
![Page 11: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/11.jpg)
Non-stationary/
Diverge
US GDP
![Page 12: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/12.jpg)
A Simple Technique to convert to Stationary
Model c as ARMA(p,q)
![Page 13: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/13.jpg)
Heteroscedasticity
Robert Engle
![Page 14: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/14.jpg)
Continuous Time Series Analysis
![Page 15: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/15.jpg)
Why?
• Interest rate• Prices for options, shares and bonds changes
continuously
![Page 16: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/16.jpg)
Modeling Continuous Time Series
W0 = 0Wt is almost surely continuous
![Page 17: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/17.jpg)
Continuous Time Series with Jump
![Page 18: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/18.jpg)
Simple Levy Process
/
![Page 19: Financial Time Series](https://reader035.vdocument.in/reader035/viewer/2022062305/5681668c550346895dda4fd6/html5/thumbnails/19.jpg)
An example to estimate parameters
is interest rate