Question

A) Describe an AR and an MA model. How are they related? (15)

B) Explain the Hoderick-Prescot filter. (15)

C) Explain how you would identify an appropriate ARIMA structure for a time series model. (20)

Answer 1

Answer A) Autoregressive Model(AR) model used to predicts future behavior of factor based on its past behavior, mainly used in time series data. It’s used for forecasting when and only there is correlation between values in a time series and the values that precede and succeed them. the model is basically just like linear regression of the factor in series against one or more past values of same data series.

Moving-average (MA) model is a model for univariate time series. This specifies that the output factor depends on linear relationship on the current as well as past values of a stochastic term. In combination with the AR model, the MA model is a special case and form general ARMA and ARIMA models of time series for complicated stochastic structure.

Answer B) The Hodrick-Prescott (HP) Filter is a data-smoothing technique, generally used for analysis to remove short-term fluctuations linked to the business cycle to reveal long-term trends. The filter help in economic forecasting linked with the business cycle.The filter use discounting concept to find the long term trend of price fluctuations.

In practice the filter process used to smooth and detrend the Conference Board's Help Wanted Index (HWI) , and benchmarked for Bureau of Labor Statistic's JOLTS.

Answer C) After making a time series stationary , the next step in fitting an ARIMA model of find the suitable model either AR or MA are required to find any short of autocorrelation that be in the time series data. By use of software like Eviews , we try different combinations of terms and observe the result. By looking at the autocorrelation function (ACF) and partial autocorrelation (PACF) plots of time series data, we can find the numbers of AR and/or MA terms that are required. The ACF plot is a bar chart of the coefficients of correlation of data and its lags. The PACF plot show the partial correlation coefficients between the time series data and its lags, explain the suitability of AR(1) model fit.