I am analyzing the Sri Lankan stock market performance during COVID-19. I considered daily stock prices from 2015 to 2021. The total number of days in the series is 2555, but 905 of them are missing records due to the stock exchange holidays. Is imputing those values based on the available data okay, or does that affect the result's accuracy to impute a large number of observations? Please give me a solution. This is the only data available for the stock market.
Imputing missing data can be useful in some cases, but it's important to consider the potential impact on the accuracy of your analysis, as a very big portion of your data is Missing. If you decide to impute the missing data, be sure to use a method that takes into account the pattern of missingness in your data. Alternatively, you may want to consider alternative methods (trends, averages) for analyzing the data or looking for alternative data sources to supplement your analysis.
Why would you want to impute data about a market for days when the market is closed? If it is closed, then there is noting to impute for that day.
Josef C Brada , I'm doing a time series analysis. In a time series, the time gap between observations should be similar, and the series should have successive data points. That is why I'm imputing missing values
Rendimal: No, I think you misnterpret the idea that time series should have successive data points based on you looking at a calendar. For example, if your time series is of daily high temperature, then for sure there should be an observation for every day, and if one were missing then it might be justified to interpolate one for that day. But stock market data never has data for Saturday and Sunday and for holidays. So interpolating data makes no sense because there should not be data for these days -- so interpolation means making up data that we know should be there - interpolating for Saturday and Sunday means making up data that does not, and should not, exist.
Yes. You can use time series models like ARIMA to impute missing values. However, the effectiveness of this approach depends on various factors such as the pattern of missingness and the underlying data generating process. Therefore, it is recommended to carefully evaluate the suitability of this method for your specific data and context.
Randimal Herath Just remove Saturdays, Sundays, and public holidays from your time series. What's the problem with that? Then you have no undesirable (and incorrect) interpolation.
I agree with Josef C Brada but since there may be a weekly seasonality, perhaps using imputation (or another method for replacing as what is used in Tramo-Seats) to handle the public holidays should be wise.
It should be noted that the analysis was carried out during working days. Seasonal fluctuations should also be investigated purely during the working period. Distortion of results will be avoided.
I presume that you are looking at returns (log (I(t)/I(t-1)) where I is the index. The log of the index is almost undoubtedly non-stationary. Usually treating the observations as continuous does not have any critical effects on your analysis. If you wish to examine the possible effects of treating the data as continuous you could add dummy variables
- D1 where there was one holiday before the observation
- D2 where there were two holidays before the observation
- D3 where there were three holidays before the observation, etc.
You could then examine the statistical significance of these variables and decide to include or exclude them depending on their effect on your results.
I am not sure that some form of imputation using for example Kalman filtering would be suitable as the behavior over the weekends and holidays will not be the same as that on work days.
The answer to your question must depend on what you want to find-out with your data. I assume that your problem is to synchronize the periodicity of the stock exchange data with possible explaining variables' data. If you want to analyse the prices as a pure stochastic process, time would, implicitly, be the only explaining variable. I think, that most (2/7=28-29%) of your missing data are due to weekends and you could handle the data as if there no weekend. But it will be necessary to adjust for the other holidays (by interpolation, possibly taking account for a weekly pattern estimated from data without those holidays, or by setting dummies).
If your explaining variables are e.g. monthly or quarterly data, I think it is better to adjust the stock exchange prices (taking monthly averages without the weekends, but with adjusted values for other holidays) instead of transforming the explaing data into weekly data (A transformation into daily data would go to far).
Completly agree with Josef C Brada. There is no need in weekends and that fact must be mentioned in the article or elsewhere.
A thought experiment: Let us assume, somebody wants to test, if and how the daily temperature influences stock prices. When temperature has its effect on the same day's price, one can simply delete the temperature values of the days with no prices (weekends and holidays) and run regressions with both time series. But if there are lagged effects - like price=a*temp+b*temp(-1) etc.+ a random variable including other effects - one cannot simply take out holidays from the temperature series, but one has to think over how to adjust the price series. This may even be necessary for weekend days, if one has the hypothesis, that Fridays' temparatures affect Mondays' prices similarily as e.g. Tuesdays' temparatures influence Fridays' prices (i.e. with a lag of 3 days). In this case, one might to think -over how to develope specifications with dummies (see John's answer).
Article The proportion of missing data should not be used to guide d...
It is generally not recommended to impute missing values in a time series when the percentage of missing observations is high (e.g., 30% or more) because it can lead to biased estimates and incorrect inferences. However, if the missing data is not completely at random (MCAR), then imputation may be appropriate. There are several methods for imputing missing values in time series data such as Last Observation Carried Forward (LOCF) and Interpolation.
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