Hi, I think you must first explain more precisely, what is not good with the results (e.g. model error is not approximately a white noise, or model fit is bad, or performance measures, such as MAE, MAPE, RMSE, are not good, or coefficients are not significant , and so). Did you check if the time series is really stationary (has no trend)? If so, and there are not any unit roots, you should use the ARMA model (without I part). What about stationarity, stability and invertibility? Did you set the appropriate order of AR and MA part (through the investigation of acf, pacf, etc).

Hi, I think you must first explain more precisely, what is not good with the results (e.g. model error is not approximately a white noise, or model fit is bad, or performance measures, such as MAE, MAPE, RMSE, are not good, or coefficients are not significant , and so). Did you check if the time series is really stationary (has no trend)? If so, and there are not any unit roots, you should use the ARMA model (without I part). What about stationarity, stability and invertibility? Did you set the appropriate order of AR and MA part (through the investigation of acf, pacf, etc).

hi Mr. Dragan and thank you for your interest

let X be the time series we are talking about

1- i checked the stationarity using KPSS test

2- results are not good in term of MAE, MAPE,..etc. and most importantly, in my model the foretasted value (of var X) is integrated into a procedure that forecast another variable (Y). when i use the real value of X i get amazing result of forecasting Y, however, when i use the foretasted value of X i get poor results for forecasting Y!

3- i did check acf, pacf,

i will try to use ARMA model.

thank you for your help.

I think that the structure of model, which forecasts the X variable and gives Xfor, is not adequate. If it would be, then the Xfor would fit well X, so most likely Yfor would be better. Try to derive more adequate structure of ARMA model. Regards, Dejan

Dear Boryana

i applied the ADF test (result quoted below)

would you please send me a link that explain your note concerning "ACF decay"?

regards;

> summary(ur.df(cv$rsi, lags=16, type='trend'))

###############################################

# Augmented Dickey-Fuller Test Unit Root Test #

###############################################

Test regression trend

Call:

lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:

Min 1Q Median 3Q Max

-1.0420348 -0.8069637 -0.3113093 0.2617201 3.0884406

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 2.38802420181 0.12172847444 19.61763 < 0.000000000000000222 ***

z.lag.1 -1.41437451726 0.06991137820 -20.23096 < 0.000000000000000222 ***

tt -0.00001231467 0.00001134956 -1.08504 0.27796

z.diff.lag1 0.43341854441 0.06688454039 6.48010 0.00000000010159203909 ***

z.diff.lag2 0.42664837233 0.06378196054 6.68917 0.00000000002521523079 ***

z.diff.lag3 0.43209041194 0.06046915014 7.14563 0.00000000000104149335 ***

z.diff.lag4 0.42293543579 0.05703911514 7.41483 0.00000000000014494384 ***

z.diff.lag5 0.40688301682 0.05336425183 7.62464 0.00000000000002971888 ***

z.diff.lag6 0.40019663881 0.04948777850 8.08678 0.00000000000000078244 ***

z.diff.lag7 0.38081547655 0.04693392119 8.11386 0.00000000000000062827 ***

z.diff.lag8 0.37999408379 0.04445187163 8.54844 < 0.000000000000000222 ***

z.diff.lag9 0.34707984784 0.04200925069 8.26199 < 0.000000000000000222 ***

z.diff.lag10 0.30049064826 0.03935206889 7.63596 0.00000000000002725154 ***

z.diff.lag11 0.02784732263 0.03654104940 0.76208 0.44605

z.diff.lag12 0.00959422782 0.03324000993 0.28863 0.77287

z.diff.lag13 0.00830523009 0.02969271226 0.27971 0.77972

z.diff.lag14 -0.00241471224 0.02574341467 -0.09380 0.92527

z.diff.lag15 0.00618586749 0.02103733342 0.29404 0.76874

z.diff.lag16 -0.00622889846 0.01499598680 -0.41537 0.67789

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9803803 on 4460 degrees of freedom

Multiple R-squared: 0.520556, Adjusted R-squared: 0.518621

F-statistic: 269.0245 on 18 and 4460 DF, p-value: < 0.00000000000000022204

Value of test-statistic is: -20.231 136.438 204.6522

Critical values for test statistics:

1pct 5pct 10pct

tau3 -3.96 -3.41 -3.12

phi2 6.09 4.68 4.03

phi3 8.27 6.25 5.34

Dear all, I completely agree with Miss Boryana's claims, it is very recommended to see some good introductory time series books. There are plenty of them, and some are even allowed to be free downloadable through the google. Best regards, Dejan

Comment on Boryana's remark of ACF decay: If ACF graph dies out slowly such as expoentially decaying, series is often nonstationary. 

Please also take a look at my working paper including some empirical examples of how to use Gretl to model many time-series regressions and interpret the results.

https://www.researchgate.net/publication/269701303_Comprehensive_Time-Series_Regression_Models_Using_GretlU.S._GDP_and_Government_Consumption_Expenditures__Gross_Investment_from_1980_to_2013

or http://ssrn.com/abstract=2540535

Generally, you have to perform unit root test to statistically determine whether time series is stationary. Next, you take a look at acf and pacf plots to identify the ARIMA orders. Third, you build some feasible models and proceed to diagnostic checking on: 1) normality, 2) autocorrelation, and 3) heteroskedasticity. Four, you compare the results and get the best fitted model, based on forecast performance and information criterion. Five, you forecast. In conclusion, I suggest you follow the Box-Jenkins approach.

Article Comprehensive Time-Series Regression Models Using Gretl—U.S....

If you have two time series, also try ARMAX (where X will be exogenous variable) and VAR.

Dear Juehui,

thank you for your valuable comment. i downloaded your working paper. i think i need to read it carefully before getting back to you. regards;

Thanks for reading. Yes, please read it thoroughly, which covers basically all related time series analysis. Please contact me if you find particular topics difficult to understand, so I can explain them to you.