[R] The auto.arima function in forecast package

[John]

Hi,

   I am wondering if I am doing correctly, but my auto.arima usually (if
not always) give me (0,1,0), whatever portion of the series I take. In the
following instances, only the last one yields ARIMA(0,1,1), and all the
other cases yield ARIMA(0,1,0). I would like to do forecast based on ARIMA.
The forecast with ARIMA(0,1,0) is exactly the random walk forecast for any
forecasting horizon h, so it does not make much sense.... Am I doing
anything wrong? Is the data very unusual?

   The length of the df_arima sequence is 68. My data is seasonally
adjusted, so I use seasonal = FALSE.

> auto.arima(df_arima, d=1, ic="aic", seasonal = FALSE)
Series: df_arima
ARIMA(0,1,0)

sigma^2 estimated as 0.9323:  log likelihood=-221.43
AIC=444.85   AICc=444.88   BIC=447.93

> auto.arima(df_arima[2:30], d=1, ic="aic", seasonal = FALSE)
Series: df_arima[2:30]
ARIMA(0,1,0)

sigma^2 estimated as 1.486:  log likelihood=-45.28
AIC=92.56   AICc=92.71   BIC=93.89
> auto.arima(df_arima[30:50], d=1, ic="aic", seasonal = FALSE)
Series: df_arima[30:50]
ARIMA(0,1,0)

sigma^2 estimated as 2.065:  log likelihood=-35.63
AIC=73.26   AICc=73.48   BIC=74.25
> auto.arima(df_arima[30:65], d=1, ic="aic", seasonal = FALSE)
Series: df_arima[30:65]
ARIMA(0,1,1)

Coefficients:
         ma1
      0.3684
s.e.  0.1591

sigma^2 estimated as 1.328:  log likelihood=-54.19
AIC=112.39   AICc=112.76   BIC=115.5


> dput(df_arima)
c(0.206955966502065, 0.572310398166964, 0.730924932354315,
1.41842200551883,
3.46103800972619, 3.61249423115895, 5.82223437508589, 4.16838241173942,
3.41346768155648, 0.862064978610255, 0.998745364906517, 0.519274399474301,
-1.11283353732583, -0.735660435061958, -0.780332562883557,
0.835729609943847,
2.72188993637388, 2.28434816118952, 1.89419627788212, 0.808622045623819,
0.628929267637468, -0.605142332415043, -1.50590253313166,
-0.288872689519148,
0.779724144195981, 1.77156391706856, 1.54853781756041, 3.31419159924959,
1.93558418905826, 1.2733744986462, 1.08821585241274, 2.62853576193935,
3.73925259835317, 4.36605858718784, 4.94030870469473, 4.95025405015856,
3.62293670685028, 2.66083271862916, 2.63088962945459, 2.64079870265661,
2.24308372288402, 4.60965981893589, 5.61665338477875, 4.13854855208327,
2.74923595127379, 1.95704807193253, 1.39700634338462, -3.2051540517546,
-4.14645815871689, -3.55954963127346, -2.75935917560429, -2.35979888878128,
-1.60997264659325, 0.107359485533354, 0.452171464181572, 1.83710430300006,
2.05388942618911, 1.42071194194746, 0.62281728667859, 0.66619920044817,
1.91899026506288, 0.876017396693274, 0.767997179685187, 0.960763098531148,
1.07168884361519, 1.7179971391635, 0.916107067445848, 0.488814956401007,
0.445930327726551, 0.700746383716555, 1.85843822164806, 0.892473264860727,
0.614568090119794, 2.4071141581713, 1.95656784524512, 1.97416030945137,
1.50143287537079, 2.16462319254254, 2.07797672518777, 0.272208427739407,
0.798064671535004, 0.754477049206304, 1.15345347401843, 1.2569270188491,
1.04667488857908, 1.61549969176582, 1.61397592409376, 2.15802281566817,
1.77514416862246, 1.37441120562698, 2.02489513295532, 2.58699935920175,
2.75245197313523, 2.23920076522477, 1.5517277192193, 2.1968256454034,
2.56612088350139, 1.58214013021238, 0.224868329892303, 0, 0.75815516785358,
0.306075421735685, -0.911618439021877, -0.851059960629386,
0.920475843398605,
0.204019124781452, 0.265049070791767, 0.693380201646732, 1.76190014304951,
1.7409678665274, 2.30875574967095, 3.1616985460498, 3.03416937102321,
2.51100317138793, 1.74651451299397, 2.1955027765292, 0.885663954102278,
0.42162278205693, -0.919995110735239, -1.09905745071531, -2.68791519080633,
-3.351439, -2.10834457783508, -2.20921682103322, -0.74375338663687,
-0.402576080931594, 1.20253696682322, 1.49061195023896, 0.526155117506621,
1.48289074384766, 0.627624111314717, 0.262639414167709, 0.101025401449073,
0.667507628973207, 0.86863891914688, 0.603620359927048, 1.53734977063493,
1.63989774985629, 2.06996035293847, 1.23150306020205, 1.00602988533123,
1.46753831297777, 1.28396719372157, 1.22372099999999, 0.42010456383097,
1.68739489046037, 1.0009947634714, 0.218850966640427, 0.218698677177565,
0.457733617597422, 1.42090579656218, 0.436897503947153, 1.05592733175737,
1.67544706250284, 2.69758588203255, 2.87640149597799, 2.13003529065778,
2.42946437023286, 2.32608159085508, 1.97956200691809, 0.274402066259904
)

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