1. FEATURES OF TIME SERIES. Explain general features of economic time series: tr
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1. FEATURES OF TIME SERIES. Explain general features of economic time series: trends, cycles, seasonality. (20 marks) 2. STATISTICS AND TIME SERIES. Figure 1 is the EViews result of hypothesis testing for auto- correlation in the growth rate of the annual working hours per employee in the United States. Is there auto-correlation in the time series? Discuss individual and joint significance of the auto- correlation. (20 marks) 3. TooLS OF THE FORECASTER. Explain in-sample assessment of the goodness of a model and out-of-sample assessment of the forecasting ability of the model. (20 marks) 4. BASIC MoDEL. (i) Define the following models: AR(p), MA() and ARMA(p.). (ii) State the Wold Decomposition Theorem. (20 marks) 5. LAG OPERATOR. Convert model Y = 1 + 0.1%-1 +Et nto an MA model. (10 marks) 6. MOVING AVERAGE PROCESS. How to check the invertibility of an MA(1) model? (10 marks) Sample: 1977 2006 Included observations: 30 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 0.737 0.73717.987 0.000 2 0.364-0.392 22.537 0.000 3 0.062 -0.058 22.676 0.000 4-0.086 0.039 22.951 0.000 5-0.162 -0.126 23.957 0.000 6-0.288-0.295 27.270 0.000 7-0.352 0.05232.432 0.000 8-0.253 0.185 35.229 0.000 9-0.064 0.001 35.416 0.000 10 0.114 0.034 36.035 0.000 Figure 1: Growth Rate in Annual Working Hours per Employee in the United States.Explanation / Answer
Please find below the components of a time series: -
Trends: - Trend is an upward or downward shift in the time series based upon the data.
Seasonality: - Seasonality refers to regularly repeating patterns of highs and lows. This usually happens during seasons like Chirstmas or Easter, for instance.
Cycles: - Cyclical time series is encountered when we see rises and falls that are not of fixed period. One can think of cycles like in a business we have business cycles. Ideally the duration of such cycles is of 2 years.
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