ARAR / ARARMA¶

Memory-shortening autoregressive models based on Brockwell & Davis (ARAR) and Parzen (ARARMA).

ARAR¶

The ARAR algorithm (Brockwell & Davis) uses a memory-shortening transformation to reduce a time series to a short-memory process, then fits an AR model.

from durbyn import ARAR

model = ARAR(max_ar_depth=13).fit(y)
fc = model.forecast(h=12, level=[80, 95])

Parameters¶

Parameter	Type	Default	Description
`max_ar_depth`	`int \\| None`	`None`	Maximum autoregressive depth
`max_lag`	`int \\| None`	`None`	Maximum lag

Note

ARAR does not use a seasonal period m.

ARARMA¶

Extends ARAR with ARMA fitting on the whitened residuals.

from durbyn import ARARMA

model = ARARMA(p=0, q=1).fit(y)
fc = model.forecast(h=12, level=[80, 95])

Parameters¶

Parameter	Type	Default	Description
`max_ar_depth`	`int`	`26`	Maximum autoregressive depth
`max_lag`	`int`	`40`	Maximum lag
`p`	`int`	`4`	AR order
`q`	`int`	`1`	MA order

AutoARARMA¶

Automatically selects the best ARARMA specification by searching over p and q ranges.

from durbyn import AutoARARMA

model = AutoARARMA(max_p=4, max_q=2).fit(y)
fc = model.forecast(h=12, level=[80, 95])

Parameters¶

Parameter	Type	Default	Description
`min_p`	`int`	`0`	Minimum AR order
`max_p`	`int`	`4`	Maximum AR order
`min_q`	`int`	`0`	Minimum MA order
`max_q`	`int`	`2`	Maximum MA order
`max_ar_depth`	`int`	`26`	Maximum autoregressive depth
`max_lag`	`int`	`40`	Maximum lag

Example¶

from durbyn import ARAR, ARARMA, AutoARARMA, compare

y_train = y[:100]
y_test = y[100:]

result = compare(
    models={
        "ARAR": ARAR(),
        "ARARMA": ARARMA(p=2, q=1),
        "AutoARARMA": AutoARARMA(),
    },
    y_train=y_train,
    y_test=y_test,
    m=1,
)

print(result.to_dataframe())