I have a time series (TS) of daily Particulate Matter (PM) data for 6 years. My PM data are not normally distributed. The result of the KPSS test returns p-value of 0.01 and t-statistic of 1.53 therefore failing the H0 of trend stationarity. The result of ADF however rejects the H0 and infers (diffrence?)stationarity.
The result of the decomposition (using slt) shows clear seasonality (please see attached image).
I used The nsdiffs and ndiffs from the R forecast package to calculate the number of seasonal differencing and regular differencing respectively to make the time series stationary. The output returned null for seasonality and 1 for regular diffrencing. Please correct me if I have done wrong so far!
forecast::ndiffs(TS[,6])
1 1
forecast::nsdiffs(TS[,6])
1 0
My question is why I get null for removing the seasonal removal if there is clear seasonality in my timeseries?
Please excuse me if my question is naive as I am new to time series analysis.
I appreciate your advise.
Best Answer
Took your 2193 daily values and introduced them to AUTOBOX which detected both a significant persistent day-of-the-week pattern :day 1 & day2 (Saturday & Sunday) ... both negative and a significant very explicable month of the year pattern (months 4-8 ... all positive and summer months BUT different) and an arima structure (1,0,0) with value .427 ALONG with a number (90) of pulses or one-time anomalies.
Other than adjust for some anomalies .... that was all that was needed to characterize it.
Your series is non-stationary that is a symptom . There are many possible causes that can lead to this symptom. One possible remedy is to adjust for two days of the week and 4 months of the year and anomalous data points. That is your remedy. Your current "procedures" to test for and to remedy non-stationarity might have assumptions regarding remedies.
From https://en.wikipedia.org/wiki/Stationary_process .... a stationary process is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance also do not change over time. Your series has a mean which changes over time due to day-of-the=week and month-of-the-year thus remedial action (model structure ) is required.
The series does not have to be otherwise different to obtain a stationary set. You should also know that if you difference a stationary series you CREATE a non-stationary series.
Here is the Actual, Fit and Forecast
with forecasts for the next 365 days here:
The model is (partially) shown here:
and also here:
&
The plot of the residuals is here:
with acf here:
Finally, the Actual & Cleansed graph highlights the anomalies which might be worth pursuing in order to identify (user)
omitted causal variables.
Hope this helps you.