Solved – How to interpolate a variable with frequency of 5 years to annual data

interpolationtime seriesunit root

I have two time-series variables: each has 14 points with an interval of 5 years. The precise years are: 

1950、1955、1960、1965、1970、1975、1980、1985、1990、1995、2000、2005、2010、2014.

I want to do the unit root test and cointegrating test for each variable. But I think the number of observations is too small. So I want to interpolate this 5-year data to annual data. Because my variables are land areas in specific years, and they are increasing year by year as the data are based on large scale and the general trend is growing.

I have tried to interpolate the data by linear interpolation: the time-series plots can be seen as below, the blue points are original points, the red ones are interpolated:

time series plot of protected area

time series plot of urban area

Because the data of one variable (protected area) are based on my spatial analysis, and each layer costs much time for PC to run. So I want to interpolate data to add observations. In other hand, because the protected area increased by a stable rate (no drop or very rapid increase), so I think even after I use spatial analysis processing to generate the data of middle years, the results won't have much discrepancy with the interpolated ones.

I want to know whether can I do this when considering the characteristics of my data and my data processing purpose. And if doing this, anything should I notice when I do time-series processing?

These was a similar question on Cross Validated: however, it hasn't be solved:
How to interpolate independent variable over five-year period?

My data are as follows: 

Year,Parea,Uarea
1950,3435829.43 ,144179.7476
1955,3619503.16 ,168028.4699
1960,3881482.63 ,196839.0495
1965,4310040.34 ,229032.161
1970,4950230.51 ,262543.7928
1975,6216028.19 ,297502.4439
1980,7062749.74 ,337481.6276
1985,8187770.34 ,381059.4338
1990,9893501.67 ,432255.4666
1995,12011196.93 ,487330.1703
2000,13327189.88 ,546829.7056
2005,15231484.09 ,612606.1358
2010,16986859.05 ,683200.605
2014,18097951.40 ,743693

Best Answer

I want to do the unit root test and cointegrating test for each variable. But I think the number of observations are too small. So I want to interpolate this 5-year data to annual data

You can't do this. You're trying to inflate the significance level of your statistical test. If you need a bigger sample, then get a bigger sample. You can't increase the sample size by interpolating.

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