# Unexpected forecasts of unemployment by auto.arima

I am building a time series model on the historical monthly unemployment data. As my data starts from 1979, my first plot indicated that I should do two split analysis - all data (from 1978 to 2021 including two big peaks of the 1980s and 1990s) and Trim Data (which is just recent 20 years - 2000 to 2021 not including the two peaks).

I ran forecasts using auto-arima.

1.

autoARIMA_State<-auto.arima(une_ts_State,stepwise = FALSE, approximation = FALSE, trace = TRUE)

2.

autoARIMA_State_trimmed<-auto.arima(une_ts_State_trimmed,stepwise = FALSE, approximation = FALSE, trace = TRUE)

forecast_State<-forecast(autoARIMA_NSW,h=55)
forecast_State_trimmed<-forecast(autoARIMA_NSW_trimmed,h=55)

Although the model fits and residuals look okay, the forecast results are flip. I get 'all data' forecast to be lower than the 'trim data' forecast which should not be the case as 'all data' clearly includes periods of way higher unemployment.

The results I obatined are:

All Data:

ARIMA(1,1,2)(1,0,1)[12]

Coefficients:
ar1      ma1     ma2    sar1     sma1
0.8692  -1.0824  0.2693  0.6268  -0.8383
s.e.  0.0584   0.0690  0.0442  0.0732   0.0512

sigma^2 estimated as 0.08271:  log likelihood=-86.6
AIC=185.2   AICc=185.37   BIC=210.58

ME      RMSE       MAE        MPE     MAPE     MASE        ACF1
Training set -0.003478117 0.2858857 0.2174171 -0.1761011 3.405361 0.270815 0.005421815

Trim Data:

ARIMA(1,0,2)(1,0,1)[12] with non-zero mean

Coefficients:
ar1      ma1     ma2    sar1     sma1    mean
0.9102  -0.2274  0.1592  0.6297  -0.8641  5.3299
s.e.  0.0311   0.0669  0.0693  0.0949   0.0694  0.0726

sigma^2 estimated as 0.06363:  log likelihood=-10.24
AIC=34.47   AICc=34.92   BIC=59.32
ME      RMSE       MAE        MPE     MAPE      MASE       ACF1
Training set 0.002565695 0.2492784 0.1924418 -0.1730198 3.600098 0.3625333 0.00389201

Forecasts: All Data

Point.Forecast
Jun 2021    5.0
Jul 2021    4.9
Aug 2021    5.0
Sep 2021    4.9
Oct 2021    5.0
Nov 2021    5.0
Dec 2021    5.0
Jan 2022    5.0
Feb 2022    5.0
Mar 2022    5.0
Apr 2022    4.7
May 2022    4.8
Jun 2022    4.7
Jul 2022    4.7
Aug 2022    4.8
Sep 2022    4.8
Oct 2022    4.8
Nov 2022    4.9
Dec 2022    4.9
Jan 2023    4.9
Feb 2023    4.9
Mar 2023    4.9
Apr 2023    4.8
May 2023    4.8
Jun 2023    4.8
Jul 2023    4.8
Aug 2023    4.9
Sep 2023    4.8
Oct 2023    4.9
Nov 2023    4.9
Dec 2023    4.9
Jan 2024    4.9
Feb 2024    5.0
Mar 2024    5.0
Apr 2024    4.9
May 2024    4.9
Jun 2024    4.9
Jul 2024    4.9
Aug 2024    4.9
Sep 2024    4.9
Oct 2024    4.9
Nov 2024    5.0
Dec 2024    5.0
Jan 2025    5.0
Feb 2025    5.0
Mar 2025    5.0
Apr 2025    4.9
May 2025    5.0
Jun 2025    5.0
Jul 2025    4.9
Aug 2025    5.0
Sep 2025    5.0
Oct 2025    5.0
Nov 2025    5.0
Dec 2025    5.0

Forecasts Trim Data:

Point.Forecast
Jun 2021    5.1
Jul 2021    5.0
Aug 2021    5.2
Sep 2021    5.2
Oct 2021    5.3
Nov 2021    5.3
Dec 2021    5.4
Jan 2022    5.4
Feb 2022    5.5
Mar 2022    5.5
Apr 2022    5.2
May 2022    5.3
Jun 2022    5.3
Jul 2022    5.2
Aug 2022    5.4
Sep 2022    5.3
Oct 2022    5.4
Nov 2022    5.4
Dec 2022    5.4
Jan 2023    5.5
Feb 2023    5.5
Mar 2023    5.5
Apr 2023    5.3
May 2023    5.4
Jun 2023    5.3
Jul 2023    5.3
Aug 2023    5.4
Sep 2023    5.3
Oct 2023    5.4
Nov 2023    5.4
Dec 2023    5.4
Jan 2024    5.4
Feb 2024    5.4
Mar 2024    5.4
Apr 2024    5.3
May 2024    5.4
Jun 2024    5.3
Jul 2024    5.3
Aug 2024    5.4
Sep 2024    5.3
Oct 2024    5.4
Nov 2024    5.4
Dec 2024    5.4
Jan 2025    5.4
Feb 2025    5.4
Mar 2025    5.4
Apr 2025    5.3
May 2025    5.4
Jun 2025    5.3
Jul 2025    5.3
Aug 2025    5.4
Sep 2025    5.3
Oct 2025    5.4
Nov 2025    5.4
Dec 2025    5.4

Sounds nice to me, until:

Although, the model fits and residuals look okay, the forecast results are flip. I get 'all data' forecast to be lower than the 'trim data' forecast which should not be the case as 'all data' clearly includes periods of way higher unemployment.

Well, both model suggest same seasonality (1,0,1), ar(1), ma(2), but first model suggest "data are moving up/down", so use differentation (1). But i see its complex.

Well according to documentation helpful things

d    Order of first-differencing. If missing, will choose a value based on test.
max.d   Maximum number of non-seasonal differences

I would guess this force d set only to 1:

2. autoARIMA_State_trimmed<-auto.arima(une_ts_State_trimmed,stepwise = FALSE, approximation = FALSE, trace = TRUE, d=1)

Just keep in mind, all other parameters can change.

(But you can look for "traditional/simple/static" methods stats::arima() or forecast::Arima() )

• Note that there are different formating options for quotations and code. Jul 15, 2021 at 9:06
• Hi! Thanks so much for your suggestions. I tried doing that autoARIMA_state_trimmed<-auto.arima(une_ts_state_trimmed,stepwise = FALSE, approximation = FALSE, trace = TRUE, d=1) It doesn't solve as I still get the similar results. Trimmed forecasts are 5ish and All Data are 4ish :( Jul 15, 2021 at 9:10
• The ARIMA fit with Trim Data also has a "with non-zero mean". I tried forcing ', allowmean=FALSE along with d=1. The forecasts are still 5ish. Jul 15, 2021 at 9:27
• @Kriti hi ..."It doesn't solve as I still get the similar results"..hm, can I ask, what is your goal? ( I mean, data from 1978 to 2021 and data from 2000 to 2021- they have different "structure" from each other... by auto arima, its get detected model selection) .. by words: "as data looked 1978 to 2021 in future it will looks according that" "as data looked 2000 to 2021" .hm..if this is for school purpose, you can do documentation, that modeling data by arima including seasonality, its structure changed over time, because "data" behave differently Jul 15, 2021 at 9:42
• Hi, this is not for school purposes. This is for a practical model I am building at work. I agree the data structure is different from 1978 to 2021 and 2000 to 2021. But thats the very reason I expect lower forcasts. The trim data has 'lower' peaks, lower volatility (st dev) that should result in a lower forcast as compared to All Data. I just dont believe this to be reasonable enough for me to proceed to the next steps. Jul 15, 2021 at 9:55