Aligning Unequal Market Calendars for Multivariate GARCH

# When the two time series with different length, how could we analysis them with a bivariate GARCH model?


# When the two time series with different length, how could we analysis them with a bivariate GARCH model?












At this moment, i need to do the analysis of rouble/us dollars exchange rate and the stock market index in Russia, I prefer to do that in a multivariate GARCH model. However, I have a question about the data. Currently, I have both data sets but they are not parallel, in other words, I have the stock market index in 30th Dec, 2014, 5th Jan, 2015, .... which is different from the exchange rate 31th Dec, 2014, 1th Jan, 13th, Jan, ..... I am not sure whether i downloaded the wrong data, otherwise, how should I deal with such case, to delete some days from both datasets?

## Answer by Alexander Didenko (score 1)

https://quant.stackexchange.com/a/16555

Usually I do one of the following:

- I change granularity of data: download weekly returns instead of daily;

- I create "super-laborious days index": I.e. (1) produce dates index consisting of all possible dates except for Sunday's and Saturday's; (2) on ALL series in dataset interpolate linearly dates, missing vs. super-index (say, on index A I have returns on A1, A2 and A7 dates, A3 were a national holiday; on B I have B1, B3 and B7: B2 were a holiday; 5 and 6 in both series are Sunday and Saturday; I create superindex C, with dates C1, C2, C3, C4 and then interpolate A3 between A2 and A4 and B2 between B1 and B3). I did that when wrote a paper about daily volatility spillovers in 12 countries across the world - many points where dates were unparalleled, as every nation has its own set of holidays.

## Answer by MD-Tech (score 1)

https://quant.stackexchange.com/a/37472

Where there are missing days in a time series, any time series, I would prefer interpolation by some method to omitting the data when you are interested in a particular granularity. Interpolating data points can be done by a number of methods depending on how you look at the world and the best fit for your data:

- Assume that the previous period's close was the same as the data for the missing period (a "flat" model)

- Linearly interpolate the data, i.e. create a straight line between previous close and next open and set the data points off the line.

- Fit a spline or moving average through the data n periods on either side and interpolate off the curve.

- fit a more complicated model to the data n periods on either side and interpolate off that model.

realistically I normally choose 2 or 3 as the best payoff to effort as they best explain the "trend" over the closed period and out of hours / auction trading.

Another answer suggests changing the granularity which I think is undesirable if you are interested in interpolating or extrapolating on a daily basis rather than based on a higher granularity as you smooth out the granular characteristics.