I don't get how you plan to convert annual data to monthly data, other than apply a 1/12 average for each month of the yearly value.

The inverse seems to be more appropriate for me - here you sum over all of the values in 12 months.

EDIT: the only thing I could see for the "year-to-month" conversion is to apply the averaged distribution of your other monthly time series, in case that the variables are equivalent or possess a heavy correlation, to the yearly value, i.e. "distribute your yearly value according to the aggregated monthly distribution of other data".

Igor Faddeenkov i dont realy understand the method that you have explained. for correlation between the series, i don't start it yet so i don't know if these series are correlated or no

i want just convert the annual data to monthly in the begennig

thank you so much for your response

When you need to convert annual financial time series data to a monthly frequency while retaining the relevant statistical properties, one commonly used method is linear interpolation. Linear interpolation assumes a linear relationship between data points and is a simple and widely used technique for filling in values between known data points. Here's how you can apply linear interpolation to convert annual data to monthly:

1. **Calculate Monthly Growth Rates:**

Compute the average monthly growth rate by taking the annual growth rate to the power of 1/12 (as there are 12 months in a year):

\[ \text{Monthly Growth Rate} = (1 + \text{Annual Growth Rate})^{1/12} - 1 \]

Calculate the annual growth rate from the existing annual data.

2. **Apply Linear Interpolation:**

For each annual data point, distribute the growth rate linearly to estimate the monthly values. Assume that the growth occurs linearly over the months between the annual data points.

For example, if you have an annual data point for January 2023 and another for January 2024, you would calculate the monthly values for February to December 2023 by applying the monthly growth rate.

3. **Check and Adjust:**

Ensure that the total of the monthly estimates equals the annual value. Adjust the estimates if needed to maintain consistency.

4. **Handle Extreme Values:**

If your annual data has extreme values, you can consider adjusting the linear interpolation to account for these extremes. For instance, you might distribute a higher proportion of the extreme value to the corresponding month.

Linear interpolation is a straightforward method, but it assumes a constant growth rate between data points, which may not always reflect the true dynamics of financial data. Depending on the nature of your financial data and the desired level of accuracy, you might explore more sophisticated interpolation techniques, such as spline interpolation or regression-based methods, which can capture non-linear patterns and better model financial time series data.

Additionally, if your financial data exhibits seasonality or other complex patterns, you may want to consider time series decomposition methods like seasonal decomposition of time series (STL) or other advanced forecasting models to accurately distribute the annual data to monthly intervals. These methods take into account the seasonal and trend components in the data to provide more accurate monthly estimations.

@Davood-Omidian yes i understand your answer, it is very important, I will try it, thank you very much

Best regards