Data

Find an appropriate set of two time series with either monthly or quarterly observations limited to up to 250 observations with no missing data. Ideally the two time series should be expected to be related in some way. Both time series should have data for the same time period.

The project should have three distinctive parts:

1. ARIMA Models.
   Investigate the statistical properties of the two univariate time series.
   Build an appropriate ARIMA model for each time series.
   
2. VAR Models
   Investigate the relationship between the two time series and build the appropriate VAR model.
3. Forecasting
   Delete the last h-observations (h is the number of forecasts) from the data file.
   Build the necessary statistical models in order to produce one set of forecasts for one of the time series: 12 months forecast for monthly data or 8 quarters forecast for quarterly data.
   For the final forecasts at least three models have to be generated: one from the ARIMA family, one from the Holt-Winters (seasonal or non seasonal), and one ARAR forecast.
   A combined forecast should be included as well and both MSE and sMAPE criteria.
   For MSE and sMAPE use the actual data values for this forecast period.
   

Text

The body of the report should be up to 5 standard pages.

Output and other material could be included in appendix but it cannot be used to overcome the 5 page text limit.

The report should be readable, not simply collection of statistical output.

 All the computations should be reproducible. E.g. include the data in Excel file, include seed #, etc.

 Methods, models and notation used should correspond to the material covered in our STAT 520 class and the Brockwell and Davis book.

Recommendations:

The report will be more valuable if the following is taken into account:

Clear explanations of what was done, how and why;

Only relevant output is included;

Clear explanation of the results and what a particular action means;

 The models are presented in an extended form and with backward shift operator form;

 Where appropriate, the following instruments should be implemented: ACF, PACF, univariate spectral analysis, tests of the residuals, cross-correlations and prewhitening, ADF unit roots test, GARCH models of the residuals.

The project must be submitted electronically in MS Word or PDF format to roumen@sc.edu.