# Noise of same order of magnitude than seasonality in a time series

everyone! I'm new in this field of statistics and I looked for an answer to this question here but couldn't find any related questions. I'm working with the Lending Club Loan Data, available on Kaggle and I'm trying to decompose a time series into trend, seasonality and noise. This is what I got using the decompose command from R, setting its type to additive. The plot on the right side is the same graph in the log scale.

The random noise seems to be of the same order of magnitude as the seasonality without even considering those strange peaks after 2014. Does this fact (noise of same magnitude as seasonality) mean the time series has no seasonality at all?

• Hi! Welcome to stackexchange! I'm trying to understand, but it's very difficult to see the actual values until 2012.. Could you either plot each part separately or plot it on a logarithmic scale ? – Tommaso Guerrini Jul 19 '17 at 15:26
• @TommasoGuerrini, just uploaded the plot in log scale. – hrmello Jul 19 '17 at 15:47

First of all welcome to StackExchange! Thank you for uploading the log scale plot which makes more clear what happens.

What decompose(ts, type = 'additive' ) does is to rewrite the time series as:

$X_t = Trend_t + Seasonal_t + Random_t$

The series you are studying has no particular seasonality and this can be seen once you detrend the series: I didn't download the data, but you can see it with:

decompose(log(ts))$x - decompose(log(ts))$trend


which corresponds to:

$log(X_t) - Trend_t = Seasonal_t + Random_t$

If you have patience just upload the that plot and then you'll see there is no periodicity (so no seasonal part there).