Hybrid MODWT-MARS model for financial time series forecasting

A hybrid model that combines maximal overlap discrete wavelet transform multiresolution analysis with multivariate adaptive regression splines to give improved one-step-ahead forecasting.

The concept of this hyrbid model was inspired from this paper by Jothimani, D., Shankar, R., Yadav, S.S.: Discrete Wavelet Transform Based Prediction of Stock Index: A Study on National Stock Exchange FiftyIndex

The premise of this model is to decompose the log-return of the closing price of a stock using MODWT multiresolution analysis and use the detail coefficients and smooth coefficient as inputs for the MARS model.

MODWT allows for decomposition of nondyadic lengthed signals and is circular-shift invariant making it suitable for financial time series prediction. It decomposes a signal in time-frequency space, exposing time-frequency information in the orignal signal not seen otherwise. Since the MODWT-MRA gives time-aligned decompositions it is used over MODWT alone.

A level 3 MODWT-MRA, using a Dauchecies least asymmetric wavelet (symlet), is performed in R using reflection of the right boundary to eliminate edge effects (padding techniques or thresholding could also be tried). A feature set is generated autoregressively by taking the 4 previous values at each time step given by the expression below. A symlet is chosen since it is a minimum phase form of daubechies and is thus causal (since it's phase angle is approximatelty linear).

At time t, value x is defined as:

This is done for the 3 detail coefficients D1, D2, D3 and the smooth coefficient S3.

Each of these are used as input for the MARS model, where Adaboost and bagging regressor boosters are used and then combined with extreme gradient boosting. The predicted coeffcient vectors are then summed up afterwards to produce the final prediction vector.

Requirments

• numpy
• pandas
• statsmodels
• pandas datareader
• datetime
• matplotlib
• scipy
• xgboost
• py-earth
• sklearn

In Sample Results:

In Sample Results (Zoomed in):

Directional Accuracy on predicted training set:

Out of Sample Results:

Out of Sample Results (Zoomed in, With one day ahead forecast):

Directional Accuracy on predicted test set with error metrics: