how to check time series data is linear or non linear

Question

I have data of idle duration of a system as follows:

Date | Idle Time Start | Idle Time End | Idle Duration |

2017/07/11 | 10:36:21 | 10:37:28 | 67 |

2017/07/11 | 10:45:44 | 10:46:58 | 74 | .......

I want to check whether the idle duration is linear or non linear using python. My second question is if I want to predict idle duration for future time then any suggestions that how can I convert this data into dataframe so that i can perform some kind of regression analysis. I have stored the idle duration and the starting of idle duration in an array. I have also plotted the data using the following code:

SampleOne, Times = get_idletime_set(1000)
FMT = '%Y-%m-%d %H:%M:%S'
Dates=[]
for i in Times:
    Dates.append(datetime.strptime(i, FMT))


plt.plot(Dates, SampleOne)
plt.ylabel('Idle Duration')
plt.xlabel('Time')
plt.show()

I got this graph. enter image description here

The obtained graph is not straight line. Does it mean that idle duration is not linear with respect to time.

Answer 1

1. excuse that i will make this a little more statistical now. So you want to check if you model look like idle = c * t + u or idle = g(t) + u (with some constant c , t as time and u as factor for everything unobserved ) right ? so first thing first, your graph is not a valide time-series graph since the dates seem not to be ordered correctly ( some line are crossing which is not correct)

2. As proposed this is imo a statistical question about modelselection. So you could run either test about linear or non-linear relationship between two variable or regress it as timeseries model without autoregressive term and compare with information criterions. But modelselection is a huge topic. Easy way would be to make an average idle time per day and regress it on a time-index as idel ~ t + t²+ln(t) in various combination and compare their performance and significance.

3. I would consider that you read up on this or propose this question as the statistical stack exchange