Interpolation of quarterly to weekly data

Question

I am currently trying to predict weekly data out of quarterly data through the so called interpolation. Unfortunately, I am having some trouble right now finding the right approach towards this, because I think the approx function in R might not be the best case for this. Do you have other approaches that I could try out to convert this accounting data from quarterly into weekly data.

Looking forward to hear suggestions.

Answer 1

Assumed Question

Given quarterly data:

1. interpolate weekly data points
2. then predict future weekly periods

Examples in R, because I absolutely love R.

Part 1. Interpolate Weekly Data Points

Example quarterly dataset from Fed:

require(tidyverse)
require(lubridate)
require(timeSeries)
require(xts)
require(tsbox)

gdp_data<- 
  tribble(
    ~DATE,      ~GDPC1, 
    20180101,   18438.254,
    20180401,   18598.135,
    20180701,   18732.72,
    20181001,   18783.548,
    20190101,   18927.281,
    20190401,   19021.86,
  ) %>% 
  mutate(DATE = ymd(alignQuarterly(ymd(DATE)))) %>% 
  ts_xts()

Resulting xts object:

> gdp_data
              GDPC1
2018-03-30 18438.25
2018-06-29 18598.13
2018-09-29 18732.72
2018-12-31 18783.55
2019-03-30 18927.28
2019-06-29 19021.86

Quarter-end periods to Week-end periods by Spline Interpolation

# create weekly time periods
weekly_dates<- 
  gdp_data %>% 
  index() %>% 
  alignQuarterly() %>% 
  align(by = "w") %>% 
  ymd() %>% 
  as.xts()

# approximate values for each week
interpolated_data<- 
  weekly_dates %>% 
  merge(gdp_data) %>% 
  na.spline() %>% 
  merge(weekly_dates, join = 'right') 

Resulting xts object:

> interpolated_data %>% tail(10)
              GDPC1
2019-04-26 18969.86
2019-05-03 18979.35
2019-05-10 18988.07
2019-05-17 18995.95
2019-05-24 19002.92
2019-05-31 19008.91
2019-06-07 19013.87
2019-06-14 19017.70
2019-06-21 19020.36
2019-06-28 19021.77

To review output as graph:

interpolated_data %>% plot()

Part 2. Predict Future Weekly Periods

Example Exponential State-space Model

require(forecast)
projection<- 
  interpolated_data %>% 
  ts_ts() %>% 
  ets('MAN', damped = F) %>% 
  predict(10)

Resulting ts forecast:

> projection
         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
2019.506       19023.17 19022.34 19024.00 19021.90 19024.45
2019.525       19024.58 19022.72 19026.44 19021.73 19027.43
2019.544       19025.98 19022.87 19029.10 19021.22 19030.75
2019.563       19027.39 19022.83 19031.95 19020.42 19034.37
2019.582       19028.80 19022.62 19034.97 19019.35 19038.24
2019.602       19030.20 19022.26 19038.15 19018.05 19042.35
2019.621       19031.61 19021.76 19041.46 19016.54 19046.68
2019.640       19033.02 19021.12 19044.91 19014.83 19051.21
2019.659       19034.42 19020.36 19048.48 19012.92 19055.92
2019.678       19035.83 19019.49 19052.17 19010.84 19060.82

To review projection as graph:

require(ggplot2)
projection %>% 
  autoplot()