Podcast
Questions and Answers
In forecasting models, what is the purpose of ARMA and GARCH models?
In forecasting models, what is the purpose of ARMA and GARCH models?
- To provide forecasts based solely on own historical observations (correct)
- To include multiple equation models for forecasting purposes
- To construct forecasting models based on gut feeling
- To test theories and investigate dynamics in detail
What is the forecasting function for an AR(1) process, $y_t = a_0 + a_1y_{t-1} + \epsilon_t$?
What is the forecasting function for an AR(1) process, $y_t = a_0 + a_1y_{t-1} + \epsilon_t$?
- $y_{t+1} = a_0 + a_1y_{t-1} + \epsilon_t$
- $y_{t+1} = a_0 + a_1y_{t-1} + \epsilon_{t+1}$
- $y_{t+1} = a_0 + a_1y_t + \epsilon_t$
- $y_{t+1} = a_0 + a_1y_t + \epsilon_{t+1}$ (correct)
What type of models provide the most accurate (out-of-sample) forecasts even if R2 is relatively low?
What type of models provide the most accurate (out-of-sample) forecasts even if R2 is relatively low?
- Models with more estimated parameters
- Parsimonious models (correct)
- Complex models with high R2
- Simple models with low R2
In forecasting, what does the true DGP stand for?
In forecasting, what does the true DGP stand for?
What is the main purpose of including other variables with predictive power in forecasting models?
What is the main purpose of including other variables with predictive power in forecasting models?
What is the key characteristic of coefficients in forecasting models?
What is the key characteristic of coefficients in forecasting models?
What is the focus of pure ARMA and GARCH models in forecasting?
What is the focus of pure ARMA and GARCH models in forecasting?
What type of models are often used to get better forecasts for asset returns and other economic variables based on historical data?
What type of models are often used to get better forecasts for asset returns and other economic variables based on historical data?
In ARMA process forecasting, what happens to prediction accuracy as the forecast horizon increases?
In ARMA process forecasting, what happens to prediction accuracy as the forecast horizon increases?
What is a property of a good prediction model in time series analysis?
What is a property of a good prediction model in time series analysis?
How are longer-horizon forecasts computed in ARMA process?
How are longer-horizon forecasts computed in ARMA process?
What is used to evaluate forecast accuracy in time series analysis?
What is used to evaluate forecast accuracy in time series analysis?
What does estimating models based on observed data introduce into future forecasts?
What does estimating models based on observed data introduce into future forecasts?
What can be computed for different forecast horizons in ARMA models?
What can be computed for different forecast horizons in ARMA models?
What is involved in comparing out-of-sample forecasts in time series analysis?
What is involved in comparing out-of-sample forecasts in time series analysis?
What can be computed for any ARMA(p,q) model using the iteration technique?
What can be computed for any ARMA(p,q) model using the iteration technique?
What can be used to conduct statistical significance testing of MSPE differences in time series analysis?
What can be used to conduct statistical significance testing of MSPE differences in time series analysis?
What are dynamic forecasts in time series analysis?
What are dynamic forecasts in time series analysis?
What are unbiased predictions for future values in ARMA models?
What are unbiased predictions for future values in ARMA models?
What decreases as the forecast horizon increases in stationary ARMA models?
What decreases as the forecast horizon increases in stationary ARMA models?
What is the purpose of using a rolling window in forecasting models?
What is the purpose of using a rolling window in forecasting models?
What is the key characteristic of coefficients in forecasting models when using a rolling window?
What is the key characteristic of coefficients in forecasting models when using a rolling window?
What does the GARCH(p,q) model allow for in forecasting?
What does the GARCH(p,q) model allow for in forecasting?
What is involved in forecast evaluation in EViews II?
What is involved in forecast evaluation in EViews II?
What can be computed for different forecast horizons in ARMA models?
What can be computed for different forecast horizons in ARMA models?
What does choosing the 'Static' option for forecasting result in, based on the empirical example using OMXH Small Cap weekly returns?
What does choosing the 'Static' option for forecasting result in, based on the empirical example using OMXH Small Cap weekly returns?
What is the focus of pure ARMA and GARCH models in forecasting?
What is the focus of pure ARMA and GARCH models in forecasting?
What decreases as the forecast horizon increases in stationary ARMA models?
What decreases as the forecast horizon increases in stationary ARMA models?
What is the main purpose of estimating models based on observed data in forecasting?
What is the main purpose of estimating models based on observed data in forecasting?
What happens to prediction accuracy as the forecast horizon increases in ARMA process forecasting?
What happens to prediction accuracy as the forecast horizon increases in ARMA process forecasting?
What can be used to conduct statistical significance testing of MSPE differences in time series analysis?
What can be used to conduct statistical significance testing of MSPE differences in time series analysis?
What is a key characteristic of a non-stationary time series?
What is a key characteristic of a non-stationary time series?
In the context of time series analysis, what does stationarity refer to?
In the context of time series analysis, what does stationarity refer to?
What is the distinguishing feature of the variance in non-stationary time series?
What is the distinguishing feature of the variance in non-stationary time series?
What happens to the sample autocorrelations in non-stationary time series?
What happens to the sample autocorrelations in non-stationary time series?
What is the null hypothesis in the Dickey-Fuller (DF) test for unit root?
What is the null hypothesis in the Dickey-Fuller (DF) test for unit root?
What does the presence of a unit root in a time series indicate?
What does the presence of a unit root in a time series indicate?
What is the key purpose of the Augmented Dickey-Fuller (ADF) test?
What is the key purpose of the Augmented Dickey-Fuller (ADF) test?
What type of time series may show a cointegrating relationship?
What type of time series may show a cointegrating relationship?
What is the impact of the lag length chosen for the ADF test?
What is the impact of the lag length chosen for the ADF test?
What is the purpose of verifying whether time series are stationary or non-stationary before conducting time series analysis?
What is the purpose of verifying whether time series are stationary or non-stationary before conducting time series analysis?
What is the main consequence of non-stationary time series in regression?
What is the main consequence of non-stationary time series in regression?
Which variables are usually stationary?
Which variables are usually stationary?
What is commonly used for lag length selection in the ADF test?
What is commonly used for lag length selection in the ADF test?
What can occur due to spurious correlation in non-stationary time series?
What can occur due to spurious correlation in non-stationary time series?
What should be included in unit root tests based on the nature of the time series?
What should be included in unit root tests based on the nature of the time series?
What can lead to a long-run equilibrium relationship among variables?
What can lead to a long-run equilibrium relationship among variables?
What is a potential issue with the ADF test?
What is a potential issue with the ADF test?
What is a complication associated with the Phillips-Perron (PP) test?
What is a complication associated with the Phillips-Perron (PP) test?
What does the KPSS test reject the null hypothesis for?
What does the KPSS test reject the null hypothesis for?
What is recommended for univariate analysis of trend stationary series?
What is recommended for univariate analysis of trend stationary series?
What is recommended for difference stationary series?
What is recommended for difference stationary series?
What may be involved in multivariate analysis if there are multiple I(1) series?
What may be involved in multivariate analysis if there are multiple I(1) series?
What type of p-values are used for accurate p-values in unit root tests according to MacKinnon (1996)?
What type of p-values are used for accurate p-values in unit root tests according to MacKinnon (1996)?
What happens if there are structural changes/breaks in time series?
What happens if there are structural changes/breaks in time series?
What does the ADF test conclude if the test value is less than -3.13 at 10% significance level?
What does the ADF test conclude if the test value is less than -3.13 at 10% significance level?
What is a potential issue with the ADF test for relatively small number of observations?
What is a potential issue with the ADF test for relatively small number of observations?
What is a general recommendation for multivariate analysis in the presence of multiple I(1) series?
What is a general recommendation for multivariate analysis in the presence of multiple I(1) series?
In the context of cointegration, what did Engle and Granger show in 1987?
In the context of cointegration, what did Engle and Granger show in 1987?
What is the implication of having both yt and zt as non-stationary, I(1), and cointegrated?
What is the implication of having both yt and zt as non-stationary, I(1), and cointegrated?
In the regression model yt = a0 + a1zt + et, what does it mean if et is not I(0)?
In the regression model yt = a0 + a1zt + et, what does it mean if et is not I(0)?
What is the key characteristic of cointegration?
What is the key characteristic of cointegration?
What is the implication of having both yt and zt as integrated of different orders (e.g., one being I(0) and the other I(1)) with a non-I(0) residual?
What is the implication of having both yt and zt as integrated of different orders (e.g., one being I(0) and the other I(1)) with a non-I(0) residual?
What did Engle and Granger receive the economics Nobel prize for in 2003?
What did Engle and Granger receive the economics Nobel prize for in 2003?
What is the significance of having both yt and zt as non-cointegrated non-stationary I(1)* variables?
What is the significance of having both yt and zt as non-cointegrated non-stationary I(1)* variables?
What is the main implication of having both yt and zt as stationary, making OLS a suitable estimator?
What is the main implication of having both yt and zt as stationary, making OLS a suitable estimator?
What is a key limitation of the Engle-Granger method?
What is a key limitation of the Engle-Granger method?
What is a distinguishing feature of the Johansen Maximum Likelihood (ML) method?
What is a distinguishing feature of the Johansen Maximum Likelihood (ML) method?
What is the purpose of the Trace Test in the context of cointegration testing?
What is the purpose of the Trace Test in the context of cointegration testing?
What is a potential issue associated with cointegration testing?
What is a potential issue associated with cointegration testing?
What is the number of cointegrating vectors in a system with n stochastic variables according to Johansen ML method?
What is the number of cointegrating vectors in a system with n stochastic variables according to Johansen ML method?
What is the focus of the Hansen instability test in the context of cointegration testing?
What is the focus of the Hansen instability test in the context of cointegration testing?
What is the main advantage of the Johansen ML method over the Engle-Granger method?
What is the main advantage of the Johansen ML method over the Engle-Granger method?
What is recommended for lag length selection in cointegration testing?
What is recommended for lag length selection in cointegration testing?
What is used to test for residual stationarity in cointegration analysis?
What is used to test for residual stationarity in cointegration analysis?
Which test is recommended for testing residual stationarity in cointegration analysis?
Which test is recommended for testing residual stationarity in cointegration analysis?
What should not be included in the tested equation for residual stationarity in cointegration analysis?
What should not be included in the tested equation for residual stationarity in cointegration analysis?
What does rejection of the null hypothesis in cointegration analysis indicate?
What does rejection of the null hypothesis in cointegration analysis indicate?
Who provides the critical values for the Engle-Granger test?
Who provides the critical values for the Engle-Granger test?
What is recommended for cointegrating regression estimation?
What is recommended for cointegrating regression estimation?
What does the FMOLS estimator aim to remove in cointegrating regression estimation?
What does the FMOLS estimator aim to remove in cointegrating regression estimation?
When is the error correction model used?
When is the error correction model used?
What is the equilibrium error in the error-correction model?
What is the equilibrium error in the error-correction model?
What do error-correction coefficients indicate in time series analysis?
What do error-correction coefficients indicate in time series analysis?
What does the VECM enable in time series analysis?
What does the VECM enable in time series analysis?
What is the purpose of the Engle-Granger method in time series analysis?
What is the purpose of the Engle-Granger method in time series analysis?
What does a cointegrating vector represent in time series modelling?
What does a cointegrating vector represent in time series modelling?
What does the equilibrium error in cointegration measure?
What does the equilibrium error in cointegration measure?
What does the OLS regression yield in the context of cointegration?
What does the OLS regression yield in the context of cointegration?
What is the focus of the Engle-Granger method in testing for cointegration?
What is the focus of the Engle-Granger method in testing for cointegration?
What implications does cointegration have in time series modelling?
What implications does cointegration have in time series modelling?
What is a potential application of cointegration in time series modelling?
What is a potential application of cointegration in time series modelling?
What are examples of potential cointegration mentioned in the text?
What are examples of potential cointegration mentioned in the text?
What does the OLS regression yield if the model is stationary in cointegration?
What does the OLS regression yield if the model is stationary in cointegration?
What is the key characteristic of the cointegrating vector in time series modelling?
What is the key characteristic of the cointegrating vector in time series modelling?
What does the equilibrium error measure in cointegration?
What does the equilibrium error measure in cointegration?
What is the key characteristic of a vector autoregressive (VAR) model?
What is the key characteristic of a vector autoregressive (VAR) model?
What is the structural form of the simpliest VAR model?
What is the structural form of the simpliest VAR model?
What is the significance of Christopher A. Sims in the context of VAR modeling?
What is the significance of Christopher A. Sims in the context of VAR modeling?
What does a VAR model illustrate about the stochastic variables it includes?
What does a VAR model illustrate about the stochastic variables it includes?
What do accumulated impulse response functions (IRFs) show?
What do accumulated impulse response functions (IRFs) show?
What is the purpose of the accumulated response of a variable to a shock?
What is the purpose of the accumulated response of a variable to a shock?
What should the accumulated IRFs converge to over the long run?
What should the accumulated IRFs converge to over the long run?
What does the accumulated response of a variable to a shock enable the interpretation of?
What does the accumulated response of a variable to a shock enable the interpretation of?
What test can be used to select the lag length in Vector Autoregression (VAR) Models?
What test can be used to select the lag length in Vector Autoregression (VAR) Models?
What does the Likelihood Ratio (LR) test assume about the test statistic distribution?
What does the Likelihood Ratio (LR) test assume about the test statistic distribution?
What does the Null hypothesis for the LR test in lag length selection state?
What does the Null hypothesis for the LR test in lag length selection state?
What is a potential issue with using the F-test on separate equations for lag selection?
What is a potential issue with using the F-test on separate equations for lag selection?
What must be the same when comparing VAR models with different lag lengths?
What must be the same when comparing VAR models with different lag lengths?
What does the LR test adjust for when estimating models?
What does the LR test adjust for when estimating models?
What distribution does the LR test assume for the errors?
What distribution does the LR test assume for the errors?
What can be used as alternative test criteria for lag length selection in VAR models?
What can be used as alternative test criteria for lag length selection in VAR models?
What can be used to test for residual autocorrelation in VAR models?
What can be used to test for residual autocorrelation in VAR models?
What can be used to test for residual normality in VAR models?
What can be used to test for residual normality in VAR models?
What does the LR test depend on for giving conclusions?
What does the LR test depend on for giving conclusions?
What can be used to evaluate forecast accuracy in EViews for VAR models?
What can be used to evaluate forecast accuracy in EViews for VAR models?
In a reduced form VAR model with a lag length of 1, how are the equations estimated?
In a reduced form VAR model with a lag length of 1, how are the equations estimated?
What is a key advantage of VAR models?
What is a key advantage of VAR models?
What is a potential limitation of VAR models?
What is a potential limitation of VAR models?
In lag length selection for monthly data, what is a suitable starting point?
In lag length selection for monthly data, what is a suitable starting point?
What constitutes the reduced form residuals in a VAR model?
What constitutes the reduced form residuals in a VAR model?
What is crucial to avoid in VAR model lag length selection?
What is crucial to avoid in VAR model lag length selection?
What is the primary characteristic of the error terms in a reduced form VAR model?
What is the primary characteristic of the error terms in a reduced form VAR model?
What is the key consideration in the selection of variables for a VAR model?
What is the key consideration in the selection of variables for a VAR model?
What is the role of feedback in a reduced form VAR model?
What is the role of feedback in a reduced form VAR model?
What is the appropriate lag length selection procedure in VAR models?
What is the appropriate lag length selection procedure in VAR models?
What is the primary requirement for the error terms in a reduced form VAR model?
What is the primary requirement for the error terms in a reduced form VAR model?
What is the primary advantage of the reduced form VAR model over the structural form?
What is the primary advantage of the reduced form VAR model over the structural form?
What is a key method to identify a VAR model by imposing a recursive ordering among the variables?
What is a key method to identify a VAR model by imposing a recursive ordering among the variables?
What can be computed for impulse response functions to show the uncertainty of the estimates?
What can be computed for impulse response functions to show the uncertainty of the estimates?
In what way can theoretical impulse response functions show asymmetry?
In what way can theoretical impulse response functions show asymmetry?
What can be used to obtain empirical examples of impulse response functions and simulate confidence bands with repetitions?
What can be used to obtain empirical examples of impulse response functions and simulate confidence bands with repetitions?
What is the expected long-term behavior of impulse response functions with stationary variables?
What is the expected long-term behavior of impulse response functions with stationary variables?
What is a way to compare the impulse response functions obtained by different orderings if there are significant correlations between error terms?
What is a way to compare the impulse response functions obtained by different orderings if there are significant correlations between error terms?
What can be used to understand the effects of shocks on the variables in time series analysis?
What can be used to understand the effects of shocks on the variables in time series analysis?
What is a potential approach to identify the VAR model and compute impulse response functions other than Choleski decomposition?
What is a potential approach to identify the VAR model and compute impulse response functions other than Choleski decomposition?
What is a way to obtain empirical examples of impulse response functions and simulate confidence bands with repetitions?
What is a way to obtain empirical examples of impulse response functions and simulate confidence bands with repetitions?
What is a method to identify a VAR model by imposing a recursive ordering among the variables based on economic theory or previous empirical examinations?
What is a method to identify a VAR model by imposing a recursive ordering among the variables based on economic theory or previous empirical examinations?
What is a way to identify the VAR model by imposing a recursive ordering among the variables based on the magnitude of correlation coefficients between error terms?
What is a way to identify the VAR model by imposing a recursive ordering among the variables based on the magnitude of correlation coefficients between error terms?
What is a method to identify the VAR model by imposing a recursive ordering among the variables based on previous empirical examinations?
What is a method to identify the VAR model by imposing a recursive ordering among the variables based on previous empirical examinations?
What is the aim of the LR test in VAR models?
What is the aim of the LR test in VAR models?
In a two-variable 1st order VAR, how many parameters are there?
In a two-variable 1st order VAR, how many parameters are there?
What is the purpose of imposing the restriction b21= 0 in VAR models?
What is the purpose of imposing the restriction b21= 0 in VAR models?
What is the focus of Granger causality in VAR analysis?
What is the focus of Granger causality in VAR analysis?
What is the purpose of innovation accounting in VAR analysis?
What is the purpose of innovation accounting in VAR analysis?
What is the implication of imposing more restrictions in a VAR model?
What is the implication of imposing more restrictions in a VAR model?
What do impulse response functions in VAR models show?
What do impulse response functions in VAR models show?
What is the aim of block-exogeneity tests in EViews for VAR models?
What is the aim of block-exogeneity tests in EViews for VAR models?
What is the purpose of including seasonal dummies in VAR models?
What is the purpose of including seasonal dummies in VAR models?
What is the significance of diagnostic checks in VAR models?
What is the significance of diagnostic checks in VAR models?
What does Granger causality imply in VAR analysis?
What does Granger causality imply in VAR analysis?
What is the purpose of identification in VAR models?
What is the purpose of identification in VAR models?
Flashcards
Forecasting in ARMA
Forecasting in ARMA
Involves predicting future values based on past observations and forecast errors.
Forecast Horizon
Forecast Horizon
The duration into the future for which predictions are made.
Dynamic Forecasts
Dynamic Forecasts
Use shorter horizon predictions to compute longer horizon forecasts.
Mean Squared Prediction Error (MSPE)
Mean Squared Prediction Error (MSPE)
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Unbiased Predictions
Unbiased Predictions
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Confidence Bands
Confidence Bands
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Rolling Window
Rolling Window
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GARCH Model
GARCH Model
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Root Mean Squared Error (RMSE)
Root Mean Squared Error (RMSE)
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Augmented Dickey-Fuller (ADF) Test
Augmented Dickey-Fuller (ADF) Test
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Phillips-Perron (PP) Test
Phillips-Perron (PP) Test
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Cointegration
Cointegration
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Engle-Granger Method
Engle-Granger Method
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Granger Causality
Granger Causality
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Impulse Response Functions
Impulse Response Functions
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Variance Decomposition
Variance Decomposition
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Stationarity
Stationarity
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Deterministic Trend
Deterministic Trend
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Structural Changes in Time Series
Structural Changes in Time Series
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Mean Absolute Error
Mean Absolute Error
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Theil U2 Coefficient
Theil U2 Coefficient
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Cointegrating Vector
Cointegrating Vector
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Block-Exogeneity Tests
Block-Exogeneity Tests
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KPSS Test
KPSS Test
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Static vs. Dynamic Forecasting
Static vs. Dynamic Forecasting
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EViews
EViews
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Forecast Evaluation
Forecast Evaluation
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Empirical Example Usage
Empirical Example Usage
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Study Notes
Forecasting in Time Series Analysis
- Forecasting in ARMA process involves predicting future values based on past observations and forecast errors
- Longer-horizon forecasts can be computed by iterating forward using forecast functions
- Prediction accuracy decreases as the forecast horizon increases in stationary ARMA models
- Prediction errors for ARMA models are not perfectly accurate and can be computed for different forecast horizons
- Forecasts are unbiased predictions for future values in ARMA models, and confidence bands can be computed for the predictions
- Forecasts can be computed for any ARMA(p,q) model using the iteration technique
- Estimating models based on observed data introduces coefficient uncertainty into future forecasts
- Comparing out-of-sample forecasts involves computing prediction errors and analyzing forecast accuracy using various criteria
- Dynamic forecasts use shorter horizon predictions to compute longer horizon forecasts
- Properties of a good prediction model include a mean of prediction errors equal to 0 and a small prediction error variance
- Mean squared prediction error (MSPE) is a key criterion for evaluating forecast accuracy in time series analysis
- Testing statistical significance of MSPE differences can be conducted using Granger-Newbold and Diebold-Mariano tests
Forecasting with GARCH Model and Forecast Evaluation in EViews II
- A rolling window involves using a fixed in-sample period to estimate a model, with the start and end dates successively increasing by one observation.
- The forecasts are based on a model estimated with the last 100 observations, even if there are more historical observations.
- Model coefficients are updated for each new prediction, which caters better for possible structural changes in the coefficients.
- GARCH(p,q) model allows for forecasting the volatility.
- After estimating the model in EViews II, one can choose between dynamic and static forecasting methods, each with its own characteristics and uses.
- Forecast evaluation in EViews II involves calculating various statistics such as Root Mean Squared Error (RMSE), Mean Absolute Error, Mean Absolute Percent Error, Theil Inequality Coefficient, Bias Proportion, Variance Proportion, and others.
- It is possible to compute the pseudo out-of-sample forecast errors and check their mean and standard deviation.
- An empirical example using OMXH Small Cap weekly returns shows the use of non-normal residuals and QML estimation, with coefficients estimates remaining significant.
- Choosing the "Static" option for forecasting in the empirical example results in unbiased forecasts with slightly more volatile actual returns than forecasted values.
- Choosing the "Dynamic" option for forecasting in the empirical example shows forecasts for return quickly converging upon the long-term unconditional mean.
- The text compares various models for one-step ahead forecasts and discusses the Theil U2 coefficient and RMSE as criteria for selecting the best model.
- The content provides detailed information on forecasting with GARCH models and evaluating forecasts using EViews II, including practical examples and statistical measures.
Unit Root Tests and Stationarity in Time Series Analysis
- Augmented Dickey-Fuller (ADF) test with 500 observations at 10% significance level concludes series is stationary around a deterministic trend if test value < -3.13
- Simulations show ADF test has relatively low power and accepts the null hypothesis of unit root too often
- ADF test may not work well with relatively small number of observations
- Phillips-Perron (PP) test suffers from similar complications as ADF test
- Structural changes/breaks in time series can complicate unit root tests and may lead to erroneous conclusions
- Empirical example using Eviews for unit root tests on Neste share total return index and U.S. default risk premium
- MacKinnon (1996) one-sided p-values are used for accurate p-values in unit root tests
- DF-GLS and KPSS are alternative unit root tests to consider
- KPSS test rejects the null of stationarity for U.S. default risk premium, indicating it is a non-stationary series
- Recommendations for univariate analysis include removing deterministic trend or including it as an explanatory variable for trend stationary series
- For difference stationary series, taking the difference is recommended
- Multivariate analysis may involve testing for cointegration if there are multiple I(1) series
Cointegration in Time Series Modelling
- Cointegration refers to a long-run relationship between variables that cannot wander away from each other over time
- It has implications for predictability, long-term dynamics, optimal portfolio allocation, and can be used to test theories such as PPP
- Examples of potential cointegration include spot and futures prices for a commodity, exchange rates, equity prices and dividends, interest rates, and housing prices
- A cointegrating vector represents the long-term equilibrium relationship between variables, and the equilibrium error measures deviations from this relationship
- The Engle-Granger method is used to test for cointegration, involving testing for the order of integration of each variable and estimating a regression
- The OLS regression yields "super-consistent" estimators of the cointegrating parameters if the model is stationary, indicating cointegration between the variables
Understanding VAR Models for Time Series Analysis
- Seasonal dummies reduce the need for lags in VAR models and are preferred by information criteria, leading to the inclusion of three seasonal dummies in the model.
- The significance of dummies can be tested using the LR test, which is not readily available in EViews.
- Different criteria suggest different lag lengths, and diagnostic checks may require the inclusion of more lags to address significant autocorrelation.
- Granger causality does not imply actual causality; it is about predictive relationships and can indicate lead-lag relationships between variables.
- Granger causality is tested using standard F-tests and block-exogeneity tests in EViews, with the aim of investigating predictive power between variables.
- Identification is not necessary for forecasting purposes, but for VAR models, the reduced form equations are estimated due to the feedback inherent in the VAR process.
- In a two-variable 1st order VAR, there are 10 parameters, and to identify the structural model, at least one restriction needs to be imposed.
- If exactly one parameter of the structural form is restricted, the system is just identified, while more restrictions lead to an over-identified system.
- Impose the restriction b21= 0 to estimate the reduced form and compute the structural parameters based on the estimated reduced form model.
- Innovation accounting in VAR analysis involves investigating dynamic interrelationships among endogenous variables and computing impulse response functions and variance decomposition to understand the effect of shocks on variable values.
- Impulse response functions, computed in practice by expressing the VAR model as a vector moving average (VMA) process, show the reactions of each variable to a given shock in the structural form.
- The formal derivations of impulse responses and variance decomposition are presented in Enders, providing a more in-depth understanding of the analysis.
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