RBI Grade B (DSIM) - Department of Statistics and Information Management · India · Reserve Bank of India Services Board
Original practice questions written to the published syllabus · not past papersModelling observations ordered in time, from classical decomposition to Box-Jenkins and beyond: stationarity, ARIMA and seasonal ARIMA, volatility models for prices, vector autoregressions, state-space models and the Kalman filter, and forecast evaluation. Agribusiness econometrics introduces ARIMA and unit roots; this subject is the full treatment.
In the exams: AICE-JRF Ag Stat Unit 2 'components of time series' (present); UPSC ISS Statistics III/IV (heavy, reported); RBI Grade B DSIM (heavy, reported); PhD course in most programmes
RBI Grade B (DSIM) (reported)
ARIMA modelling, unit-root tests, ARCH/GARCH, VAR and cointegration, and forecast evaluation for economic and financial series.
How our questions for RBI Grade B spread across the units of Time Series Analysis. Difficulty: 23 easy, 41 medium, 10 hard.
| Forecast accuracy: MAPE, RMSE and the Diebold-Mariano test | 10 | |
| Box-Jenkins ARIMA: identification, estimation and diagnostic checking | 9 | |
| Unit-root tests and structural breaks | 9 | |
| Vector autoregression and cointegration | 9 | |
| Stationarity, autocorrelation and partial autocorrelation functions | 8 | |
| AR, MA and ARMA processes | 8 | |
| Seasonal ARIMA and ARIMAX with weather covariates | 8 | |
| ARCH and GARCH models for price volatility | 8 | |
| Smoothing: moving averages and exponential smoothing (Holt-Winters) | 5 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
The sample ACF of a monthly price series starts near 0.95 and declines very slowly and almost linearly over 30 lags. What should the analyst do first?
A. Difference the series
A slow, nearly linear decay is the signature of non-stationarity (a unit root); the series should be differenced (and tested formally) before identifying ARMA orders. An MA(30) is grossly over-parameterised, and the ACF clearly rules out white noise.
Further reading: Box, Jenkins, Reinsel and Ljung, Time Series Analysis
A stationary series has rho(1) = 0.6 and rho(2) = 0.5. What is the partial autocorrelation at lag 2?
D. 0.219
phi(2,2) = (rho2 - rho1^2)/(1 - rho1^2) = (0.5 - 0.36)/0.64 = 0.219. Forgetting the denominator gives 0.140; 0.500 is the ordinary autocorrelation; 0.360 is rho1 squared, the lag-2 ACF an AR(1) would imply.
Further reading: Box, Jenkins, Reinsel and Ljung, Time Series Analysis
Why is a random walk, Y(t) = Y(t-1) + e(t) with e(t) white noise, not stationary even though its expected change is zero?
A. Its variance grows with time
Starting from Y(0), Var(Y(t)) = t sigma^2, which grows without limit, so the variance is not constant. The mean stays at Y(0) with no drift; the shocks are white noise; and the first difference is white noise, which is stationary.
Further reading: Box, Jenkins, Reinsel and Ljung, Time Series Analysis
The process Y(t) = 4 + 0.6 Y(t-1) + e(t) is stationary. What is its mean?
B. 10
mu = c/(1 - phi) = 4/0.4 = 10. 4 is the constant, not the mean; 6.67 = 4/0.6; 2.4 = 4 x 0.6.
Further reading: Box, Jenkins, Reinsel and Ljung, Time Series Analysis; Brockwell and Davis
What is the order of the stages in the Box-Jenkins approach to model building?
A. Identification, estimation, diagnostic checking, then forecasting
Box and Jenkins proposed an iterative cycle: identify a tentative model, estimate it, check the residuals, and return to identification if the checks fail; forecasting follows once the model is adequate.
Further reading: Box, Jenkins, Reinsel and Ljung, Time Series Analysis
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?
C. Difference Y and X together and fit the regression with AR(1) errors
If the error needs differencing, all variables in the regression are differenced, then the regression is fitted with ARMA (here AR(1)) errors. Differencing Y only changes the meaning of b1; OLS in levels risks spurious regression.
Further reading: Box, Jenkins, Reinsel and Ljung, Time Series Analysis; Hyndman and Athanasopoulos
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?
D. A spurious regression between non-stationary series
Granger and Newbold showed that regressing independent random walks gives high R-squared and very low Durbin-Watson; R-squared above DW is a warning sign. The fit says nothing about a real relation unless the series are cointegrated.
Further reading: Enders, Applied Econometric Time Series; Hamilton, Time Series Analysis
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?
C. 4.0
Unconditional variance = omega/(1 - alpha - beta) = 0.2/0.05 = 4.0. Dividing by 1 - beta only gives 1.33; dividing by alpha + beta gives 0.211.
Further reading: Enders, Applied Econometric Time Series
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?
A. LM = 12; ARCH effects are present
LM = n R-squared = 200 x 0.06 = 12 > 9.49, so the null of no ARCH is rejected. Dividing by the number of lags or using R-squared x 100 gives 3 or 6, both below the critical value, and wrongly accepts the null.
Further reading: Enders, Applied Econometric Time Series
Two I(1) price series are said to be cointegrated when:
B. Some linear combination of them is stationary
Cointegration means a linear combination is I(0), so the series share a long-run equilibrium. Being I(1) individually is the precondition, not the definition; high correlation and Granger causality are neither necessary nor sufficient.
Further reading: Enders, Applied Econometric Time Series; Hamilton, Time Series Analysis
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