Long-run wavelet-based correlation for financial time series free download

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J Finance 7 1 —91 Google Scholar. Examining the level-one details, it appears there is a reduction of variance in the period of the Great Moderation. There is a variance changepoint identified in This example does not correct for the delay introduced by the 'db2' wavelet at level one. However, that delay is only two samples so it does not appreciably affect the results. To assess changes in the volatility of the GDP data pre and post , split the original data into pre- and post-changepoint series.

Obtain the wavelet transforms of the pre and post datasets. In this case, the series are relatively short so use the Haar wavelet to minimize the number of boundary coefficients. Compute unbiased estimates of the wavelet variance by scale and plot the result. From the preceding plot, it appears there are significant differences between the preQ2 and postQ2 variances at scales between 2 and 16 quarters. Because the time series are so short in this example, it can be useful to use biased estimates of the variance.

Biased estimates do not remove boundary coefficients. Use a 'db2' wavelet filter with four coefficients. The results confirm our original finding that the Great Moderation is manifested in volatility reductions over scales from 2 to 16 quarters. You can also use wavelets to analyze correlation between two datasets by scale.

Examine the correlation between the aggregate data on government spending and private investment. The data cover the same period as the real GDP data and are transformed in the exact same way.

Government spending and personal investment demonstrate a weak, but statistically significant, negative correlation of The multiscale correlation available with the MODWT shows a significant negative correlation only at scale 2, which corresponds to cycles in the data between 4 and 8 quarters.

Even this correlation is only marginally significant when adjusting for multiple comparisons. The multiscale correlation analysis reveals that the slight negative correlation in the aggregate data is driven by the behavior of the data over scales of four to eight quarters.

When you consider the data over different time periods scales , there is no significant correlation. With financial data, there is often a leading or lagging relationship between variables. In those cases, it is useful to examine the cross-correlation sequence to determine if lagging one variable with respect to another maximizes their cross-correlation. To illustrate this, consider the correlation between two components of the GDP -- personal consumption expenditures and gross private domestic investment.

Personal expenditure and personal investment are negatively correlated over a period of quarters. At longer scales, there is a strong positive correlation between personal expenditure and personal investment.

Examine the wavelet cross-correlation sequence at the scale representing quarter cycles. The finest-scale wavelet cross-correlation sequence shows a peak positive correlation at a lag of one quarter. This indicates that personal investment lags personal expenditures by one quarter. Using discrete wavelet analysis, you are limited to dyadic scales.