Linear interpolation on fixed dates using Python

Here's a way to do it just with datetime and calendar. It's rather lengthy though, beware.

First, we need a method to make the desired time series

Months and quarters are a bit tricky, which date is one month after January 31, for example? But a method could look like this:

For testing, I included the generation of random values that belong with the dates.

from datetime import datetime, timedelta, date
import calendar
from random import random

def makeseries(startdate):
    datesA = [startdate] # collect the dates in this list
    valsA = [random()]   # and the randomly generated 'data' in this one
    date = startdate    

    # add days
    step = timedelta(1)
    while date - startdate <= timedelta(91):
        date += step
        datesA += [date]
        valsA += [random()]

    # add months
    step = timedelta(30)
    while date - startdate <= timedelta(2*365):
        if date.month in [1,3,5,7,8,10,12]:
            date += timedelta(1)
        elif date.month == 2:
            date -= timedelta(2)
        date += step
        datesA += [date]
        valsA += [random()]

    # add quarters
    step = timedelta(91)
    while date - startdate <= timedelta(int(365*10)):
        date += step
        if date.year % 4 == 0:
            date += timedelta(1)
        datesA += [date]
        valsA += [random()]

    # add years
    step = timedelta(365)
    while date - startdate <= timedelta(int(365*50)):
        date += step
        if date.year % 4 == 0:
            date += timedelta(1)
        datesA += [date]
        valsA += [random()]

    return datesA, valsA

Then, a simple method to find the nearest date to a given date in a series of dates

def findIndexOfNearest(series, D):
    # returns the index of the date in series that is closest to, but greater than D
    for i, date in enumerate(series):
        if date > D:
            return i
    return None

Generate the two time series, plus some mock date for the first series

thisyear = datetime.today().year
quarterEndMonth = (datetime.today().month+2)//3*3
quarterEndDay = calendar.monthrange(thisyear, quarterEndMonth)[1]

d1,v1 = makeseries(date.today())
d2,_ = makeseries(date(thisyear,quarterEndMonth, quarterEndDay))
v2 = []

Interpolate using timedeltas and print the interpolated values

for d in d2: 
    i = findIndexOfNearest(d1, d)
    if i:
        prev = d1[i-1]
        next = d1[i]
        prevRatio = 1-(d-prev).total_seconds()/(next-prev).total_seconds()
        nextRatio = 1-(next-d).total_seconds()/(next-prev).total_seconds()
        interp = prevRatio*v1[i-1] + nextRatio*v1[i]
        v2 += [interp]
        print("%s = %.2f * %s + %.2f * %s" % (d, prevRatio, prev, nextRatio, next))
        print("%17.2f * %10.2f + %.2f * %10.2f = %.2f" % \
               (prevRatio, v1[i-1], nextRatio, v1[i], interp))
    else: # date to be interpolated is past last original date
        v2 += [v1[-1]]
        print("%s = 1.00 * %s = %24.2f" % (d,d1[-1],v1[-1]))

Some example output:

Here, the original series just switched to 3-month gaps, with one date in November, and another in February the next year. The date for which we are interpolating is in December.

                     original           original
                      date                date
                        v                   v
2014-12-02 = 0.69 * 2014-11-04 + 0.31 * 2015-02-03
     ^       0.69 *       0.95 + 0.31 *       0.10 = 0.69
     |         ^           ^       ^           ^       ^
     |         |        original   |       original   interpolated 
date from      |         value     |         value       value
2nd series   weight              weight