TS_Fall_2011_Lecture_5

TS_Fall_2011_Lecture_5 - FIN 271 FINANCIAL MODELING AND...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
FIN 271 FINANCIAL MODELING AND ECONOMETRICS LECTURE SET 5 TIME SERIES MODELING REFIK SOYER THE GEORGE WASHINGTON UNIVERSITY
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 AUTOREGRESSIVE INTEGRATED MOVING AVERAGE PROCESSES. • ARIMA(p,d,q) Processes Nonstationary Processes Ê Difference stationary TS (or unit root series): Differenced series is stationary. If is not stationary, but if the first differences of ]] tt W( 1 B ) ttt 1 t œ] ] œ ] is stationary then we may represent W by a stationary ARMA process. t Example: The Dow Jones data (Random Walk) ]] œG 1 t % ] t is not stationary, but the first differenced series is white noise. Ê] can be represented by an ARIMA(0,1,0) model. t 1
Background image of page 2
3 In general, if is an ARIMA(p,d,q) process, then ] t is nonstationary, but the d th differences of the series ] ] tt W( 1 B ) d œ ] can be represented by an stationary ARMA(p,q) process. What do we mean by d th differences ? d1 W ( 1B ) œÊ œ ] ] œ] ttt 1 t d 2 (1 B)W W W ( ) ( ) (1 B) œ œ ] ] ] œ ] t 1 t t 1t 1 t 2 t 2  If is described by an ARIMA(p,d,q) process then we write ] t 9) % (B) (1 B) (B) . ] œ d Equivalently, W , the d th difference of the series can be represented by a stationary and invertible ARMA process % (B)W (B) œ where W (1 . d ] 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 If the differenced series has nonzero mean, the we can write 9) % (B) W (B) . tt œ where W W . œ . Examples : • ARIMA (0, 1, 1): ]] œ   1 t1 t 1  .% ) % • ARIMA (1, 1, 0): ( ) ( ) œG ] ] t 1 t1 t2 t 9% (1 B) (1 B) Ê] œ G ] t 1 t EX. Price of the Crude oil. • ARIMA (1, 1, 1): ( ) ( )   t t 1t1 ) % (1 B) (1 (1 B) Ê ] œ G % 1t 1 t • How about higher order differencing ? Ex. d 2 (SAS Example Analysis of PIRC data). œ 3
Background image of page 4
Analysis of PIRC Data OPTIONS LS=80; *QUARTERLY TIME SERIES; DATA IRCALL; INFILE 'C:\TSDATA\IRC.TXT'; INPUT IRC PIRC YD RCP RAAA; PROC ARIMA; IDENTIFY VAR=PIRC; IDENTIFY VAR=PIRC(1); IDENTIFY VAR=PIRC(1,1); RUN; Pl ot 60 80 100 120 140 160 180 200 0 10 20 30 40 50 60 70 80 90 110 PI RC 1 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Name of variable = PIRC. Standard deviation = 32.27038 Number of observations = 101 Autocorrelations Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 0 1041.378 1.00000 | |********************| 1 987.826 0.94858 | . |******************* | 2 933.834 0.89673 | . |****************** | 3 881.977 0.84693 | . |***************** | 4 833.674 0.80055 | . |**************** | 5 789.514 0.75814 | . |*************** | 6 745.101 0.71549 | . |************** | 7 703.467 0.67552 | . |************** | 8 662.211 0.63590 | . |************* | 9 623.851 0.59906 | . |************. | 10 588.171 0.56480 | . |*********** . | 11 554.106 0.53209 | . |*********** . | 12 521.008 0.50031 | . |********** . | 13 489.406 0.46996 | . |********* . | 14 457.373 0.43920 | . |********* . | 15 425.996 0.40907 | . |******** . | 16 393.545 0.37791 | . |******** . | 17 360.578 0.34625 | . |******* . | 18 328.828 0.31576 | . |****** . | 19 297.590 0.28577 | . |****** . | 20 268.327 0.25767 | . |***** . | 2 5
Background image of page 6
Name of variable = PIRC. Period(s) of Differencing = 1. Standard deviation = 1.6697 Number of observations = 100 NOTE: The first observation was eliminated by differencing. Autocorrelations Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 0 2.787899 1.00000 | |********************| 1 2.140614 0.76782 | . |*************** | 2 2.070001 0.74249 | . |*************** | 3 1.800982 0.64600 | . |************* | 4 1.558508 0.55903 | . |*********** | 5 1.604676 0.57559 | . |************ | 6 1.525965 0.54735 | . |*********** | 7 1.411033 0.50613 | . |********** | 8 1.323173 0.47461 | . |*********. | 9 1.139464 0.40872 | . |******** . | 10 1.101324 0.39504 | . |******** . | 11 0.980445 0.35168 | . |******* . | 12 0.920560 0.33020 | . |******* . | 13 1.058342 0.37962 | . |******** . | 14 0.990563 0.35531 | . |******* . | 15 1.114757 0.39986 | . |******** . | 16 1.079192 0.38710 | . |******** . | 17 1.009858 0.36223 | . |******* . | 18 0.924783 0.33171 | . |******* . | 19 0.828745 0.29727 | . |****** . | 3 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Name of variable = PIRC. Period(s) of Differencing = 1,1. Mean of working series = 0.029293 Standard deviation = 1.12216 Number of observations = 99 NOTE: The first 2 observations were eliminated bydifferencing.
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 39

TS_Fall_2011_Lecture_5 - FIN 271 FINANCIAL MODELING AND...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online