ARIMA Forecasting PartI
The
forecasting methods can be broadly
divided into two categories: quantitative and qualitative methods. The
quantitative forecasting literature is dominated by two sub categories of
methods: noncausal time series models and the causal econometric approaches.
The difference between them is whether the forecasting model identifies any
causal relationship between the dependent variable and its influencing factors.
De Gooijer & Hyndman (2006) reviewed the
past 25 years of research into time series forecasting and found one third of
all papers concerned used time series forecasting. They have classified the
papers according to the models as: exponential smoothing, ARIMA, Seasonality,
State space and structural models and the Kalman filter, Nonlinear models, Long
memory models, ARCH/GARCH models and Count data forecasting. Forecasting in the
past four decades is dominated by the integrated autoregressive movingaverage
models (ARIMAs) proposed by Box and Jenkins (1970). Depending on the frequency
of the time series, either simple ARIMA or seasonal ARIMA (i.e. SARIMA) models are mostly used.
Prior to understanding the ARIMA, following are few things to understand:
1.
A basic understanding and intuition of stationary is required.
2.
Understanding of an Autoregressive
process (AR) process.
3.
Understanding of Moving Average (MA) process.
4.
Understanding of mixed model of ARMA.
Basic intuition on Stationary property of a time series.
Here
is a video in which, I tried to explain the stationary property of a time series
in the least technical way just to shed the light or develop a basic intuition.
References:
De Gooijer, J. G., &
Hyndman, R. J. (2006). 25 Years of Time Series Forecasting. International
Journal of Forecasting, 22(3), 443–473.
doi:10.1016/j.ijforecast.2006.01.001
Box, G. E. P. and G. M. Jenkins (1970) Time series analysis: forecasting and control, Holden Day, San Francisco.
Fantastic articles is post by you in this blog. You give a nice thing. Thank you for such a nice article. Every word of this blog helps me to give detail to me.
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Thank you.
DeleteDear Shishir,
ReplyDeleteFirstly, sorry if I am bothering you.
My problem is I use Stata software for building Seasonal Arima model (sorry again because I don't use R software) and I don't know how to write the full model in equation from the Stata results.
I show you the results below. Hope you can help me. Thank you in advance, Shishir!
arima sxh_m, arima(1,0,0) sarima(1,0,1,12)
ARIMA regression
Sample: 2000m1  2014m12 Number of obs = 180
Wald chi2(3) = 738.45
Log likelihood = 959.4371 Prob > chi2 = 0.0000

 OPG
sxh_m  Coef. Std. Err. z P>z [95% Conf. Interval]
+
sxh_m 
_cons  101.9032 51.05939 2.00 0.046 1.828592 201.9777
+
ARMA 
ar 
L1.  .7795168 .0356272 21.88 0.000 .7096887 .8493449
+
ARMA12 
ar 
L1.  .9334173 .1179918 7.91 0.000 .7021577 1.164677

ma 
L1.  .802917 .1693845 4.74 0.000 1.134905 .4709294
+
/sigma  49.30807 1.341556 36.75 0.000 46.67866 51.93747

Note: The test of the variance against zero is one sided, and the twosided confidence interval is truncated at zero.
Dear Nguyễn Đỗ Quốc Thống,
ReplyDeleteThank you for the query. Can you see my blog on ARIMA and SARIMA. I have the equations written there...
Thank you very much Shishir Shakya for your response.
DeleteI understood what stationery is, but I dont understand why we need a stationery series for time series forecasting. Can you explain? Thanks.
ReplyDeleteStationary makes data unit root free. Well, for the forecasting stationary may/maynot require it depends upon your requirements. I am for sure for proper forecasting you should be able to predict out of sample data.
ReplyDelete