Effect of Kalman Filter and Smoother on Forecasting of Financial Time Series

Abstract

The main objective of this work is preprocessing of financial time series data by using state space models. Financial time series data is highly volatile, that is, there are large variations in a small time. For a forecasting model, this type of nature of financial time series creates trouble in recognising pattern. Here, Kalman filter and Kalman smoother are used to reduce the noise from the actual observations. Kalman filter removes sharp variations up to some extent, so that the forecasting capability of a model can be improved. Kalman smoother is a form of Kalman filter which filters data from both sides. After filtering/smoothing, data has low variations and when this data is applied to a forecasting model, root mean square error is reduced and coefficient of determination is increased. We briefly discuss some time series modelling techniques, such as autoregressive(AR), moving average(MA) and autoregressive conditional heteroscedastic(ARCH) models for forecasting of financial data. We also discuss the use of artificial neural network(ANN) for non-linear time series. These models are applied to stock price data of five companies and RMSE values are observed. We then discuss Kalman filter and Kalman smoother along with their state space representations. An example of Kalman filter is also presented. The models ARMA, GARCH and ANN are applied to the daily closing price data of five companies(TATA motors, NTPC, HZL, IGL and SAIL). Data is collected from National Stock Exchange(NSE) from 1 February 2012 to 30 January 2014. Filtered data and smooth data are obtained from original data by using Kalman filter and Kalman smoother respectively. To observe the effect of filtering and smoothing, first original data is forecasted using the above mentioned forecasting models and then filtered and smooth data is used for forecasting by using these models. Forecasting in all the three cases is compared in terms of root mean square error(RMSE). We observe that the reduction in RMSE values after using Kalman filter is very significant in the case of ARMA and GARCH models. Though the reduction is observed very similar when Kalman smoother is used. The reduction by using Kalman filter is also observed when ANN is applied for forecasting. But interestingly, the reduction in RMSE value is further observed when Kalman smoother is used.