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import xarray as xr
import numpy as np

# create an example dataset
da = xr.DataArray(np.random.rand(10,30,40), dims=['time', 'lat', 'lon'])

# define a function to compute a linear trend of a timeseries
def linear_trend(x):
    pf = np.polyfit(x.time, x, 1)
    # we need to return a dataarray or else xarray's groupby won't be happy

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def open_date_file(file_path):
    df = pd.read_csv(file_path, index_col=0, parse_dates=True)
    df['BeginDate'] = df.BeginDate.apply(lambda t: pd.to_datetime(t, format='%Y-%m-%d'))
    return df


var = sys.argv[1]
path = ''
max_lag = 30
type_ls = ['split', 'displ']

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# implement my own aggregation downsampling function

from itertools import product
import numpy as np
import xarray as xr

def aggregate(data, factor=2, mean=True):
    ndim = data.ndim
    shape = data.shape
    # promote single value to list

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def longest_com_period_possible(xa_list):
    """Determine the longest common period for list of xarrays
    
    Parameters
    ----------
    xa_list: list of xarray dataarrays
    
    Returns
    -------
    period: slice

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def autocorr(x, t=1):
    """Calculates autocorrelation with lag = 1.
    
    Parameters
    ----------
    x: numpy.array
        Input
    
    Returns
    -------

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