Time Series Analysis - unevenly spaced measures - pandas + statsmodels

Question

I have two numpy arrays light_points and time_points and would like to use some time series analysis methods on those data.

I then tried this :

impor         


        

Answer 1

seasonal_decompose() requires a freq that is either provided as part of the DateTimeIndex meta information, can be inferred by pandas.Index.inferred_freq or else by the user as an integer that gives the number of periods per cycle. e.g., 12 for monthly (from docstring for seasonal_mean):

def seasonal_decompose(x, model="additive", filt=None, freq=None):
    """
    Parameters
    ----------
    x : array-like
        Time series
    model : str {"additive", "multiplicative"}
        Type of seasonal component. Abbreviations are accepted.
    filt : array-like
        The filter coefficients for filtering out the seasonal component.
        The default is a symmetric moving average.
    freq : int, optional
        Frequency of the series. Must be used if x is not a pandas
        object with a timeseries index.

To illustrate - using random sample data:

length = 400
x = np.sin(np.arange(length)) * 10 + np.random.randn(length)
df = pd.DataFrame(data=x, index=pd.date_range(start=datetime(2015, 1, 1), periods=length, freq='w'), columns=['value'])

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 400 entries, 2015-01-04 to 2022-08-28
Freq: W-SUN

decomp = sm.tsa.seasonal_decompose(df)
data = pd.concat([df, decomp.trend, decomp.seasonal, decomp.resid], axis=1)
data.columns = ['series', 'trend', 'seasonal', 'resid']

Data columns (total 4 columns):
series      400 non-null float64
trend       348 non-null float64
seasonal    400 non-null float64
resid       348 non-null float64
dtypes: float64(4)
memory usage: 15.6 KB

So far, so good - now randomly dropping elements from the DateTimeIndex to create unevenly space data:

df = df.iloc[np.unique(np.random.randint(low=0, high=length, size=length * .8))]

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 222 entries, 2015-01-11 to 2022-08-21
Data columns (total 1 columns):
value    222 non-null float64
dtypes: float64(1)
memory usage: 3.5 KB

df.index.freq

None

df.index.inferred_freq

None

Running the seasonal_decomp on this data 'works':

decomp = sm.tsa.seasonal_decompose(df, freq=52)

data = pd.concat([df, decomp.trend, decomp.seasonal, decomp.resid], axis=1)
data.columns = ['series', 'trend', 'seasonal', 'resid']

DatetimeIndex: 224 entries, 2015-01-04 to 2022-08-07
Data columns (total 4 columns):
series      224 non-null float64
trend       172 non-null float64
seasonal    224 non-null float64
resid       172 non-null float64
dtypes: float64(4)
memory usage: 8.8 KB

The question is - how useful is the result. Even without gaps in the data that complicate inference of seasonal patterns (see example use of .interpolate() in the release notes, statsmodels qualifies this procedure as follows:

Notes
-----
This is a naive decomposition. More sophisticated methods should
be preferred.

The additive model is Y[t] = T[t] + S[t] + e[t]

The multiplicative model is Y[t] = T[t] * S[t] * e[t]

The seasonal component is first removed by applying a convolution
filter to the data. The average of this smoothed series for each
period is the returned seasonal component.