markov-regime-switching

Modelling regime switching index price movements with markov chains.

1. Given Specifications

1. Forecast horizons: for quarterly GDP growth try a nowcast (h=0, all indicators of that quarter are known) and forecast horizons h=1 to 4 quarters. For the year-on-year inflation rate, try forecast horizons h=1 to h=12 months.

2. Use a recursive out-of-sample forecast experiment. For each horizon h, use such an experiment to generate forecasts of the first quarter/month of 2000 to the last quarter/month of 2021. This will make your forecasts comparable to each other. In addition, think about sensibly defined subsamples.

3. Use at least the following three loss functions:

   • mean forecast error
   • mean absolute forecast error
   • root mean squared forecast error.

   [We want to evaluate density forecasts, so we will use loss functions such as CRPS aswell.]

2. TODO

• Use oxford realized values to evaluate volatility forecasts.

• Use code from ATSA to get the best static fat-tailed distribution to describe vola.

• Use PCA and extract dynamic factor, then research if the dynamic factor can be forecasted usefully, then try to use that factor in a markov switching model (parameter).

• Can we use something like gibbs sampling or the like (MCMC) together with such a dynamic factor (exogeneous var)?

Use MS over MS-DFM ?

(+) Can be used to construct direct density forecasts. However in the MS-DFM the estimated factor and transition probabilities can be used in a subsequent model, like an ADL to construct forecasts.

(+) Simpler. MS doesn't require a Kalman-Filter or the like to estimate probabilities.

(+) Avoids multivariate distr. modelling/normality assumption

(-) Can't use external information, i.e. dynamic factor (except if we use two-dimensional target vector) to estimate the regime.

(?) Can we use a custom loss function, where only the density of one indicator (S&P) is considered?

Usage

1. Download the data specified in Data Sources to some folder.
2. Copy the sample config file to config.py and set value appropriately.

3. Data Sources

• S&P data set by Robert Shiller: Website, Download. The stock price data are monthly averages of daily closing prices.

Fred Data Sources

All FRED data sources were downloaded in .csv format.

• Industrial Production Total Index: Website, downloaded as .csv.

• Producer Price Index by Commodity: All Commodities (PPIACO)

• Moody's Seasoned Baa Corporate Bond Yield (BAA) Website

• Moody's Seasoned Aaa Corporate Bond Yield (AAA) Website

4. Useful commands:

activate markov-switching conda install

conda list -e > requirements.txt