ICAR-IASRI MSc and PhD Time Series Analysis: practice questions

1 · Seasonal ARIMA and ARIMAX with weather covariates · medium

A model of monthly milk procurement is Y(t) = b0 + b1 X(t) + n(t), where X(t) is a fodder-price index and n(t) follows an ARIMA(1,1,0) process. How is the model estimated correctly?

1. Fit an ARIMA to Y and then add X to the forecasts afterwards
2. Difference Y only and keep X in levels in the regression
3. Difference Y and X together and fit the regression with AR(1) errors
4. Fit ordinary least squares to the levels and ignore n(t) entirely

2 · Seasonal ARIMA and ARIMAX with weather covariates · medium

A government imposes an export ban on onions that permanently lowers the level of domestic prices from a known month. How should the ban enter an intervention model?

1. As a pulse variable, 1 in the ban month and 0 in every other month
2. As a step variable, 0 before the month and 1 from it on
3. As a seasonal dummy repeated in the same month every year
4. As an additive outlier deleted from the series before modelling

3 · Unit-root tests and structural breaks · medium

A regression of one district's wheat price on an unrelated district's cotton area, both trending random walks, gives R-squared = 0.92 and a Durbin-Watson statistic of 0.25. What is the most likely explanation?

1. Perfect multicollinearity between the two regressors
2. Heteroscedastic errors with no autocorrelation
3. A genuine long-run relationship confirmed by the high R-squared
4. A spurious regression between non-stationary series

4 · ARCH and GARCH models for price volatility · medium

A GARCH(1,1) model for weekly returns has omega = 0.2, alpha = 0.10 and beta = 0.85. What is the unconditional variance of returns?

1. 1.33
2. 0.211
3. 4.0
4. 0.222

5 · ARCH and GARCH models for price volatility · medium

Engle's LM test regresses squared residuals from a price-return model on 4 of their own lags, with n = 200 and R-squared = 0.06. The 5 per cent critical value of chi-square with 4 df is 9.49. What is the conclusion?

1. LM = 12; ARCH effects are present
2. LM = 12; but the test needs an F table, not chi-square
3. LM = 3; no ARCH effects at 5 per cent
4. LM = 6; no ARCH effects at 5 per cent

6 · ARCH and GARCH models for price volatility · easy

In volatility modelling, how is the return on a commodity price usually defined?

1. P(t) / P(t-1) without any transformation
2. The average price over the previous twelve months
3. P(t) - P(t-1) in rupees per quintal
4. log P(t) - log P(t-1)

7 · Vector autoregression and cointegration · easy

Two I(1) price series are said to be cointegrated when:

1. Both become stationary after first differencing
2. Some linear combination of them is stationary
3. One of them Granger-causes the other in a VAR
4. Their correlation coefficient exceeds 0.9 in levels

8 · State-space models and the Kalman filter · easy

In the Kalman filter, what happens to the Kalman gain when the observation-noise variance becomes very large relative to the prediction variance?

1. The gain approaches one
2. The gain becomes negative
3. The gain is unaffected
4. The gain approaches zero

9 · Spectral analysis (introduction) · easy

What does the spectrum of white noise look like?

1. Rising with frequency
2. Flat across all frequencies
3. A peak at the seasonal frequency only
4. A single sharp peak at frequency zero

10 · Forecast accuracy: MAPE, RMSE and the Diebold-Mariano test · hard

Two price-forecasting models are compared on 100 out-of-sample periods. The mean squared-error loss differential is 0.6 and its long-run variance is estimated as 4.0. What is the Diebold-Mariano statistic, and what is the conclusion at 5 per cent?

1. DM = 15; the models differ in accuracy
2. DM = 0.15; the models do not differ in accuracy
3. DM = 3.0; the models differ in accuracy
4. DM = 0.3; the models do not differ in accuracy