check this link maybe help you

https://core.ac.uk/download/pdf/11984117.pdf

Dear Rais, divisia monetary aggregates are better than simple-sum monetary aggregates because they control for the degree of substitutability/ complementarity among the monetary sub-aggregates. For doing so, they include temporal weights that depend on temporal relative interest rate differentials. Simple-sum aggregates do not consider these relationships at all. Many studies do find them better for many applications. After returning back to the "non-conventional" monetary policy -MP- (old economists like me will always consider it as the "really conventional" MP) and before returning back again to the modern conventional ST-interest-rate-based MP, William Barnett's & Apostolos Serletis' divisia aggregates should be given their well deserved position in Monetary Theory.

Here are a few papers that explore the usefulness of appropriately measured monetary aggregates:

• El Shagi, M. & Kelly, L. (Forthcoming), 'What can we learn from country level liquidity in the EMU', Journal of Financial Stability.
• Kelly, L. J.; Barnett, W. A. & Keating, J. W. (2011), 'Rethinking the liquidity puzzle: Application of a new measure of the economic money stock', Journal of Banking & Finance 35(4), 768--774.
• El-shagi, M.; Kelly, L. J. & others (2014), 'Liquidity in the liquidity crisis: evidence from Divisia monetary aggregates in Germany and the European crisis countries', Economics Bulletin 34(1), 63--72.
• El-shagi, M.; Kelly, L. J. & others (2014), 'Liquidity in the liquidity crisis: evidence from Divisia monetary aggregates in Germany and the European crisis countries', Economics Bulletin 34(1), 63--72.
• Kelly, L.; Binner, J. M.; Chang, C. L. & Tseng, Y. H. (2014), 'Monetary policy in Taiwan: the implications of liquidity', Lee, D. and Gregoriou, G., Handbook of Asian Finance: Financial Markets and Sovereign Wealth Funds 1, 221--237.
• El-Shagi, M.; Giesen, S. & Kelly, L. J. (2015), 'The quantity theory revisited: A new structural approach', Macroeconomic Dynamics 19(1), 58--78.
• Keating, J. W.; Kelly, L. J.; Smith, A. L. & Valcarcel, V. J. (2019), 'A model of monetary policy shocks for financial crises and normal conditions', Journal of Money, Credit and Banking 51(1), 227--259.

The idea of divisia money aggregates seems to be appealing. However, when I compared divisia indices to the standard M1, M2, M3 aggregates, it appeared that the results (out-of-sample CPI forecasting) are fairly identical. I tested Polish data only, so it is likely that you will get different results. Check it empirically as divisia theoretically should be better measure of broad money.

Paweł Baranowski Out-of-sample CPI forecasting is difficult in low inflation economies. I think the reason why Divisia monetary aggregates have a difficult time improving forecasting performance is that in low inflation economies there is very little money driven inflation. Moreover, Divisia money is not overly available in high inflation countries. But it might be fun to gather data from low and high inflation countries, calculate Divisia and simple sum aggregates and test how the predictive power on money changes?