Evolutionary-based return forecasting with nonlinear STAR models: evidence from the Eurozone peripheral stock markets

Abstract

Traditional linear regression and time-series models often fail to produce accurate forecasts due to inherent nonlinearities and structural instabilities, which characterize financial markets and challenge the Efficient Market Hypothesis. Machine learning techniques are becoming widespread tools for return forecasting as they are capable of dealing efficiently with nonlinear modeling. An evolutionary programming approach based on genetic algorithms is introduced in order to estimate and fine-tune the parameters of the STAR-class models, as opposed to conventional techniques. Using a hybrid method we employ trading rules that generate excess returns for the Eurozone southern periphery stock markets, over a long out-of-sample period after the introduction of the Euro common currency. Our results may have important implications for market efficiency and predictability. Investment or trading strategies based on the proposed approach may allow market agents to earn higher returns.

Appendix

For the DM test we use the squared forecast errors $(e_{0,t}^2 ,e_{i,t}^{2}), t=1,\ldots , n$. The null hypothesis of equality of expected forecast performance is given by

$$\begin{aligned} \hbox {E}(e_{0,t}^2 ,e_{i,t}^2 )=0 \end{aligned}$$

(23)

Defining $d_t =(e_{0,t}^2 ,e_{i,t}^{2}), t=1,\ldots , n$, the test is based on the sample mean

$$\begin{aligned} \bar{{d}}=n^{-1}\sum \nolimits _{t=1}^{n} d_t \end{aligned}$$

(24)

As the sequence of forecast errors follows a moving average process of order (h–1) the autocorrelations of order h or higher are zero (Harvey et al. 1997). The variance of $\bar{d}$ is asymptotically given

$$\begin{aligned} V(\bar{d})\approx n^{-1}\left[ \gamma _0 +2\sum \nolimits _{k=1}^{h-1}\gamma _\kappa \right] \end{aligned}$$

(25)

where $\gamma _{\kappa }$ is the k-th autocovariance of $d_t$. The Diebold–Mariano test statistic is provided by the following score function

$$\begin{aligned} DM=\left[ \hat{V}(\bar{d})\right] ^{-1/2}\bar{d}\;\hbox { with }\; DM \sim N(0, 1) \end{aligned}$$

(26)