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How does one

  1. write the mathematical equation for the ARIMA(1,1,1) model with the estimated coefficients below and
  2. use the ARIMA(1,1,1) model and time series points below to produce a forecast value for time = 41 (e.g. the forecast value for t = 41 is 18)?

    auto.arima(deseasonal_cnt, seasonal=FALSE)

    Series: deseasonal_cnt
    ARIMA(1,1,1)

    Coefficients:

      ar1     ma1
      0.5510  -0.2496 
    

    s.e. 0.0751 0.0849

    sigma^2 estimated as 26180: log likelihood=-4708.91
    AIC=9423.82 AICc=9423.85 BIC=9437.57

    airplane[35:40]
    19.2981 17.1230 16.1230 18.1352 19.3401 18.1414

    fitted(Arima(airplane, c(1,1,1)))[35:40]
    18.3492 18.3752 17.8322 18.7924 19.8253 18.8198

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    $\begingroup$ Check out similar questions on this site and you will find a dozen answers. $\endgroup$ Apr 27 '18 at 7:22
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All ARIMA models can be expressed in a similar form to this enter image description here

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    $\begingroup$ What do your variables $Y$, $X$, $a$ refer to? They don't seem to connect with anything named in the question, so some explanation is needed. $\endgroup$
    – whuber
    May 14 '18 at 21:40
  • $\begingroup$ Y is the observed dependent series (endogenous) and the X's are possible exogenous series either user-specified or analytically developed (pulses/level shiftts/trends.seasonal pulses)... none in this case. $\endgroup$
    – IrishStat
    May 14 '18 at 22:22

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