auto.arima "no suitable ARIMA model found" for measuring dependency between debt and GDP

Question

In my studies I've been working recently on dependency between debt and GDP growth in USA from 1966 to 2015. I used logged and differenciated GDP time series data and combined it with 0/1 debt-to-GDP time series data which takes value 0 when the debt-to-GDP level is below some arbitrary value and 1 when it's above. I have made 41 such arrays, depending on arbitrary level, and tried to estimate ARIMA model through auto.arima method in "forecast" library and then I'd like to select the best model selecting the best information criterion (let's say Akaike).

However, using auto.arima on series returned with No suitable ARIMA model found. Could somebody tell what is the reason for it and how can I estimate it?

Here is the data I use:

gdp time series:

Time Series:
Start = 1966 
End = 2015 
Frequency = 1 

               gdp
 [1,] 8.150000e+11
 [2,] 8.617000e+11
 [3,] 9.425000e+11
 [4,] 1.019900e+12
 [5,] 1.075884e+12
 [6,] 1.167770e+12
 [7,] 1.282449e+12
 [8,] 1.428549e+12
 [9,] 1.548825e+12
[10,] 1.688923e+12
[11,] 1.877587e+12
[12,] 2.085951e+12
[13,] 2.356571e+12
[14,] 2.632143e+12
[15,] 2.862505e+12
[16,] 3.210956e+12
[17,] 3.344991e+12
[18,] 3.638137e+12
[19,] 4.040693e+12
[20,] 4.346734e+12
[21,] 4.590155e+12
[22,] 4.870217e+12
[23,] 5.252629e+12
[24,] 5.657693e+12
[25,] 5.979589e+12
[26,] 6.174043e+12
[27,] 6.539299e+12
[28,] 6.878718e+12
[29,] 7.308755e+12
[30,] 7.664060e+12
[31,] 8.100201e+12
[32,] 8.608515e+12
[33,] 9.089168e+12
[34,] 9.660624e+12
[35,] 1.028478e+13
[36,] 1.062182e+13
[37,] 1.097751e+13
[38,] 1.151067e+13
[39,] 1.227493e+13
[40,] 1.309373e+13
[41,] 1.385589e+13
[42,] 1.447764e+13
[43,] 1.471858e+13
[44,] 1.441874e+13
[45,] 1.496437e+13
[46,] 1.551793e+13
[47,] 1.615526e+13
[48,] 1.669152e+13
[49,] 1.739310e+13
[50,] 1.803665e+13

debt (50% threshold):

     debt%gdp
 [1,]        0
 [2,]        0
 [3,]        0
 [4,]        0
 [5,]        0
 [6,]        0
 [7,]        0
 [8,]        0
 [9,]        0
[10,]        0
[11,]        0
[12,]        0
[13,]        0
[14,]        0
[15,]        0
[16,]        0
[17,]        0
[18,]        0
[19,]        0
[20,]        0
[21,]        0
[22,]        0
[23,]        0
[24,]        1
[25,]        1
[26,]        1
[27,]        1
[28,]        1
[29,]        1
[30,]        1
[31,]        1
[32,]        1
[33,]        1
[34,]        1
[35,]        1
[36,]        1
[37,]        1
[38,]        1
[39,]        1
[40,]        1
[41,]        1
[42,]        1
[43,]        1
[44,]        1
[45,]        1
[46,]        1
[47,]        1
[48,]        1
[49,]        1
[50,]        1

Then I intersect them and put into auto.arima model.

Answer 1

I encountered a similar problem when I was trying to run auto.arima with one of my explanatory variables. I took the square root of the variable and auto.arima worked just fine. The problem might be that the values in your GDP variable might be too large and might be creating a numerical overflow.