How to deal with missing value in a time series stock market data?

Question

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 1

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)