ARIMA Error – Solving auto.arima Error Due to Singular System in R

arimaforecastingr

I am trying to fit a dynamic forecasting model using auto.arima but I am getting the following error when trying to run my code:

'Error in solve.default(res$hessian * n.used, A) : Lapack routine dgesv: system is exactly singular: U[1,1] = 0'

Here is my code:

library(forecast)

v1 <- c(1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
v2 <- c(0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
v3 <- c(1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)
v4 <- c(1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)

dynamicmatrix <- data.matrix(cbind(v1,v2,v3,v4))
dynamicmatrix

ts <- ts(dynamicmatrix[,1], start=c(2036,2))
dynamicmatrix <- data.matrix(dynamicmatrix[,-1])
fit <- auto.arima(ts, xreg=dynamicmatrix[])

The first column of dynamicmatrix contains the data that I want to forecast. The other 3 columns contain the data for xreg.

Does anyone know what might be causing this error?

Thank you,
Niels

Best Answer

v1 = v2 + v3. So there is a redundant predictor causing a singular regression.

Related Solutions

Logistic – Why Exact Singularity When Adding Dummy Variable to Multinomial Logistic Using R mlogit?

I think I have discovered the source of the error. In my model, as well as in the example above, the dummy is an individual specific attribute, but I had included it in the model statement as an alternative specific attribute.

Properly specifying the dummy as an individual-specific attribute (i.e. after the '|') produces a sensible result:

summary(mlogit(choice ~ pf + cl + loc + wk + tod + seas | odd.dummy-1 , data=Electr)) # Dummy as individual-specific attribute

Coefficients :
             Estimate Std. Error  t-value Pr(>|t|)    
pf          -0.624054   0.023369 -26.7048   <2e-16 ***
cl          -0.108130   0.008281 -13.0577   <2e-16 ***
loc          1.442730   0.050706  28.4527   <2e-16 ***
wk           0.997726   0.044911  22.2157   <2e-16 ***
tod         -5.454041   0.185186 -29.4517   <2e-16 ***
seas        -5.831122   0.188030 -31.0116   <2e-16 ***
odd.dummy:2  0.057435   0.067904   0.8458   0.3976    
odd.dummy:3  0.064776   0.068510   0.9455   0.3444    
odd.dummy:4  0.061038   0.067753   0.9009   0.3676

I'll leave it to someone else to try to explain the mathematics of what was happening.

R – Resolving mlogit Error: ‘System is Exactly Singular’ in Logistic Regression

You don't want multinomial logit as your dependent variable is a score that is nearly continuous. I would start by plotting the data e.g. with

with(nicotine, stripchart(jitter(active)~score, vertical = TRUE))

which doesn't reveal any obvious pattern.

Then you could look at a linear model:

m1 <- with(nicotine, lm(score~as.factor(active)))
summary(m1)

(this is equivalent to the t-test you ran) which shows a small and nonsignificant difference. Plotting m1 doesn't reveal anything particularly interesting to my eyes, either. You say you found large differences in variances but

with(nicotine, sd(score[active == 1]))
with(nicotine, sd(score[active == 0]))

shows the difference to be not all that large (and the stripchart shown above agrees).

Then you could add mp to the model:

m2 <- with(nicotine, lm(score~as.factor(active) + mp))
summary(m2)

which also shows only very small differences and a miniscule $R^2$

There's probably other things you could do, but it looks like there is not much to find here.

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