Inflation Forecasting

Monetary Policy Committee (MPC) (RBI) came out with a press release on December 4, 2020, stating that, Consumer Price Index (CPI) inflation is projected at 6.8% for Q3:2020-21, 5.8%  for Q4:2020-21. 

According to the press release, the inflation outlook has turned adverse due to supply-side bottlenecks and large margins being charged to the consumer; food prices at elevated levels (cereal and vegetable prices may soften); crude oil prices picking up on optimism of demand recovery. 

The outlook provided by RBI in its’ Monetary Policy Report October 2020 was 5.4% in Q3 and 4.5% in Q4.

The inflation forecasts at RBI are generated using a variety of models and the modeling and forecasting approaches are constantly reviewed and refined. A recent working paper by RBI throws some light on the challenges faced by central banks in inflation forecasting, “Inflation forecasting has become a more challenging task due to weakening of the traditional link between inflation and economic activity across countries for a variety of factors such as greater external openness, volatile exchange rates and commodity prices, increased competition from e-commerce, and potential non-linearities”.  

In this blog post, I have attempted to forecast the inflation trajectory for Q3 and Q4 2020-21 using an autoregressive model. For this purpose, I have used monthly inflation data from August 2016 to November 2020. The data for this period has been used because, in August 2016, India adopted an inflation target of 4% until March 2021 with an upper tolerance level of 6% and a lower limit of 2%. So the data under this period falls under the same regime of “inflation targeting”. The central government in consultation with RBI is set to review this inflation target by the end of March 2021. 

Autoregressive model (on the first difference of inflation data) using a seasonal lag

The model that I have used for inflation forecast be stated as follows:

In the above equation x(t) represents inflation at the time “t”.  x (t-1) represents inflation at time (t-1)

and so on. To explain if, x(t) is CPI inflation in November 2020, then x(t-1)) is inflation in October 2020

and x(t-12) is inflation in November 2019. β1 and β2 are the slope coefficients of the independent variables

{x (t-1)- x(t-2)} and {x(t-12)-x(t-13)}. The above equation is a transformed version of an

autoregressive model wherein I have taken the first difference of the inflation time series as a

dependent variable and also included a seasonal lag in the equation. The first difference means the

difference between the value of the time series in the current period and the previous period.

Seasonal lag is the value of the independent variable which is exactly one year before the dependent

variable. Such transformation is required to make the data “covariance stationary” and also

remove “seasonality” from the data.

To explain this model in another way, if x(t) is the inflation in November 2020, then this model is

explaining the difference between the inflation of Nov-20 and Oct-20 using the data on the difference

between the inflation of Oct-20 and Sep-20 and also the data on the difference between the inflation of

Nov-19 and Oct-19.

Regression Results:

Using the data from Aug-16 to Nov-20 (including data from July -15 to July-16 for the lag terms),

my regression results on the above model are as follows:

Regression Results
R Square	0.3055
Standard Error	0.0055
Observations	52
Significance F	0.000132
	Intercept	X(t-1)-X(t-2)	X(t-12)-X(t-13)
Coefficients	0.0003762	0.0539658	-0.644941
P-value	0.628119	0.679368	0.000141

The regression does not have a very high R square. Intercept and x(t-1)-x(t-2), both have high

p-values and are not significant. However, the F-statistics is significant and hence I use the results for

forecasting.

I tested the autocorrelations of the residuals of the model for up to 12 lags. For each lag, the t-statistics

were insignificant which indicates the model does not have seasonality. I also tested the

model for Autoregressive Conditional Heteroskedasticity (ARCH (1)) and the results show that the

model does not have heteroskedasticity.

Inflation Forecasts:

Using the regression for forecasting xt -x(t-1) and then solving for x(t), I get the following forecasts for

inflation.

Dec’-20	5.76%
Jan'-21	5.58%
Feb'-21	6.27%
Mar'-21	6.82%

Q3 20-21	6.77%
Q4 20-21	6.22%

Two months of actual inflation data (Oct-20 and Nov-20) is included in Q3 forecasts and it is close to MPC projections, Q4 forecast

is higher by about 40 basis points than the MPC projections.

Limitations of the model

In this model, we have first arrived at the forecast for the inflation for Dec20 and then used the Dec-20

forecast for Jan-21 and so on. In this type of forecasting, with each successive forecast, the uncertainty

associated with the forecast goes on increasing. The model assumes that the future values are related to

past values which may be inaccurate if the market conditions are changing rapidly.

References: RBI website, CFA Institute

Disclaimer: I am not an expert in forecasting. This is my first attempt to forecast inflation and hence the model and the methodology used by me may not be accurate. I welcome feedback on the model at tulsyananimesh@gmail.com.The blog post is not meant to provide any professional advice and written with the purpose to discuss a forecasting and analytical methodology. The methodology has various limitations and some of them have been discussed above. Any investment action you take based upon the analysis presented here is strictly at your own risk. The forecast, analysis, and views presented here do not reflect the ideologies, or views of any organization with which I am affiliated or potentially affiliated. Despite best efforts to present authentic information, the blog post is likely to suffer from errors and omissions. I am eligible to modify, update, or delete the information on this blogpost.