Handling Different Market Calendars in Multivariate Price Series
Summary
The document considers how to align closing-price histories for indices traded on exchanges with different holidays and weekly schedules. It outlines several treatments for missing observations and explains the trade-offs of each. Keeping only dates shared by all markets avoids fabricated values but reduces the sample and discards available observations. Forward-filling preserves a common calendar, though it records a zero move during the gap followed by a combined move when trading resumes. Linear interpolation spreads the change across missing dates but can introduce artificial serial correlation in returns.
For multivariate analysis, the answer also suggests resampling joint returns from nearby comparable observations or sampling from a fitted joint return distribution. These approaches preserve some distributional features but depend on finding suitable matches or specifying a defensible model; random draws can produce implausible values, while filling with a mean dampens variance. The document offers a menu rather than prescribing one method. The appropriate choice depends on the analysis, and any imputed series should be treated with awareness of the artifacts each method can introduce.
Key ideas
- Using only dates shared by all markets avoids imputation but reduces sample size and loses observations.
- Forward-filling can turn holiday gaps into zero returns followed by a larger recorded move.
- Linear interpolation may smooth gap-related jumps while creating artificial serial correlation.
- Joint-return resampling can preserve distributional features but requires comparable observations.
- Parametric sampling depends on model fit, while mean imputation can dampen variance.
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Full text
# How to deal with missing value in a time series stock market data? # How to deal with missing value in a time series stock market data? I have collected data for the period of 2002 to 2018 for following indices Nifty (India), NASDAQ (US), ADX (UAE) and TASI (Saudi Arabia). After collection, I have arranged data in a single sheet with the date and closing price for all the four indices. As we know the working days differ for stock markets there are missing dates between each countries. For example, It is a holiday for Saudi Arabia and UAE stock exchanges on Fridays, whereas it is working day for the other two exchanges. Kindly, let me know how to deal with this missing values. What I felt is to copy and paste the closing price of previous days closing for missing periods. Is it the right approach? or is there any other alternatives. ## Answer by user25064 (score 7, accepted) https://quant.stackexchange.com/a/41175 Some approaches - Use only common points - Exclude all holidays in any index. Reduced sample size Loss of information No 'made up' data (consistency) - Fill forward - use previous day as you suggested. Issue here is that jumps in the market over holidays are recorded as zero change then a big change. - Linear interpolation - linearly interpolate the price as a function of time. This helps with the jumps present in the fill forward method but may lead to an increase in serial correlation of returns that is a pure artifact of this method. - Resampling - because you only have 4 indices that you are looking at you could emperically resample the joint distribution of returns in a window around the gap that you're looking to fill. Basically look for a day nearby that is as similar as possible where all indices are available in change space (return space) and use that as the change from previous price in your missing index. Issue here is that there may not be a very similar day in your dataset Also you are in a sense "making up" data at this point Should maintain similar distributional properties - Parametric sampling - Fit the joint distribution of returns from the available data and sample from that to fill the points Subject to model fitting issues (EG if you assume joint normal distribution but your sample is not IID) You are subject to the randomness of the universe, you may receive an outlandish sample. To combat this you could fill with the mean but this has the effect of dampening variance. If someone finds this answer and is looking for issues of investment histories that differ in length then you may be interested in Stambaugh (1997)
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