# GRETL. (Gnu Regression, Econometrics and. Time-series Library)

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1 1 GRETL (Gnu Regression, Econometrics and Time-series Library)

2 2 In this project you should analyze generated and real data. Analysis of each set of data should contain: a) Descriptive statistics. b) Time series plot. c) Checking of normality. d) If data are non-stationary take, for example log-differences to assure stationarity. e) Descriptive statistics, time series plot, checking of normality, analysis of stationarity of new data. f) Analysis of correlogram, finding AR and MA processes order. g) Estimating ARMA processes (in gretl) h) Compare estimated models using information criterions. i) Choosing the best ARMA model. j) Estimating ARMA-GARCH processes (in Ox) k) Compare estimated models using information criterions. l) Choosing the best ARMA-GARCH model.

3 3 Projekty oddajemy w wersji papierowej. Kazdy projekt bedzie "broniony" indywidualnie. W projekcie prosze zamiescic kolejne kroki dochodzenia do ostatecznego modelu (co obserwujemy, jakie modele beda rozpatrywane w zwiazki z tym, jakie sa kryteria wyboru optymalnego modelu itd, warto porobic troche rysunkow) Which financial time series features do you observe? Which class of models do you chose and why? What are the probably orders of the models? Which model is the best for given data? Is it really the best existing model? wygenerowane dane pochodza z modeli poznanych na wykladzie -ARMA + szeroka klasa modeli GARCH z roznymi efektami + rozne rozklady warunkowe rzedy modeli sa zdroworozsadkowe czyli zawiaraja sie w ARMA(2,2), GARCH(2,1) proponowane narzedzia do analizy to GRETL oraz OX z pakietem

4 4 1. How to get and install gretl a) Go to page or and download gretl (Section Gretl for Windows, gretl exe)

5 5 b) Install gretl with default parameters After that, gretl will be installed, but usually in Polish language, to run gretl in English language you have to click: Narzędzia -> Ustawienia -> Ogólne or Tools -> Preferences -> General Choose Wybór języka dla GUI -> English

6 Choose Wybór języka dla GUI -> English or Language Preserence -> Polish 6

7 7 2. To load data to gretl from ASCI (text) file, you have to choose from menu: File -> Open data -> Import -> Text/CSV When gretl loads chosen file it will open window with question about structure of data. Answer Yes a) Choose Time series, then click Forward b) Choose Daily (5 days), then click Forward c) Type 1970/01/01 as a starting date, then click Forward (any other date will do) d) Click Apply (if everything is OK).

8 8

9 9

10 right mouse button 10

11 11 3. To load data to gretl from Excel file: File -> Open data -> Import -> Excell Gretl will open first window, click Yes. Then it will open next window with the same question like previous, so you have to choose the same steps.

12 5. With loaded and set data you can: a) Get a time series plot: click with right mouse button second variable name (first is a constant added by gretl) and choose Time series plot b) Get a descriptive statistics: click with right mouse button and choose Descriptive statistics c) Get a correlogram: click with right mouse button and choose Correlogram (you have to choose a proper lag, in most cases the default lag will be good) After choosing lag two windows will open, first with graph of autocorrelation and partial autocorrelation, second with coefficient of autocorrelation and partial autocorrelation functions (with significance of each coefficient). 12

13 13 6. Transformations of variables: a) returns: Add -> Define new variable In opened window type: new_variable = (x x(-1))/x(-1) where x name of variable b) logarithmic returns: Add -> Log differences of selected variables

14 14

15 15 8. Checking of normality: Variable -> Frequency distribution Variable -> Frequency distribution-> Against Normal Q-Q plot for rates 6 y = x Normal quantiles

16 16 The lower the p-value, the less likely the result is if the null hypothesis is true, and consequently the more "significant" the result is, in the sense of statistical significance. One often rejects the null hypothesis when the p-value is less than 0.05 or 0.01, corresponding respectively to a 5% or 1% chance of rejecting the null hypothesis when it is true (Type I error).

17 17 9. Checking AR and MA processes order: Variable -> Correlogram other data than APATOR!! ACF for Data /T^ lag PACF for Data /T^ lag

18 Estimating ARMA processes: a) Model -> Time series -> ARIMA b) Choose dependent variable.

19 H0: parameter insignificant p-value<0.05 reject H0 19

20 You can save the residuals of model by choosing Save->Residuals in the window with models characteristics

21 21 ACF for uhat /T^ lag PACF for uhat /T^ lag

22 TEST of ARCH effect in residuals 22

23 GARCH models 23

24 GARCH model 24

25 Example data_gretl.xls 25

26 Density 26 Example data_gretl.xls 30 Test statistic for normality: Chi-squared(2) = pvalue = Data N( , ) Data

27 27 Example data_gretl.xls ACF for Data /T^ lag PACF for Data /T^ lag

28 28

29 29

30 30 Residual ACF /T^ lag Residual PACF /T^ lag

31 31

32 32 check the normality of ARMA residuals do the ARCH test

33 33 Test for normality of residual - Null hypothesis: error is normally distributed Test statistic: Chi-square(2) = with p-value = 1.88e-005

34 34

35 35 Test for ARCH of order 5 - Null hypothesis: no ARCH effect is present Test statistic: LM = with p-value = P(Chi-square(5) > ) = e-018 Test for ARCH of order 5 coefficient std. error t-ratio p-value alpha(0) e e-012 *** alpha(1) e-08 *** alpha(2) * alpha(3) alpha(4) *** alpha(5) ***

36 36

37 Density standardized residuals Test statistic for normality: Chi-squared(2) = pvalue = uhat6 N( ,1.0021) uhat6 37

38 squared residuals of ARMA model 38

39 39 squared standardized residuals ACF for usq /T^ lag PACF for usq /T^ lag

40 Density 40 if it is not Gaussian distribution we need t-student distribution or skewed t-st leverage effect OX Test statistic for normality: Chi-squared(2) = pvalue = uhat6 N( ,1.0021) uhat6

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Multiple Regression Analysis in Minitab 1 Suppose we are interested in how the exercise and body mass index affect the blood pressure. A random sample of 10 males 50 years of age is selected and their

### Cointegration and the ECM

Cointegration and the ECM Two nonstationary time series are cointegrated if they tend to move together through time. For instance, we have established that the levels of the Fed Funds rate and the 3-year