Having used Rob Hyndman’s forecasting package in R, I decided to give Facebook’s Prophet package a spin and do a comparison of the results.

##Forecasts using Prophet

The Time-series data sets: - Daily data set

##    y         ds
## 1  8 2016-05-10
## 2 10 2016-05-11
## 3  3 2016-05-11
## 4  7 2016-05-12
## 5  3 2016-05-12
## 6  3 2016-05-12

Prophet provides the ability to forecast projected growth based on market intel, by specifying the carrying capacity ‘cap’; the forecast should reach the maximum/saturation at the set ‘cap’. For this data set, I’ve set the cap at 7 units/day, but the forecaster can choose to set it at an increasing/decreasing sequence.

daily_Data_wgrowth <- daily_data %>% 
  mutate(cap = 7)
head(daily_Data_wgrowth)

##    y         ds cap
## 1  8 2016-05-10   7
## 2 10 2016-05-11   7
## 3  3 2016-05-11   7
## 4  7 2016-05-12   7
## 5  3 2016-05-12   7
## 6  3 2016-05-12   7

Visualize the daily timeseries

ggplotly(ggplot(daily_data, aes(x = ds, y = y)) + geom_line(color = "firebrick") + ggtitle("Daily Timeseries")) 

Functions calling function prophet that fits and returns the model, then predicts on the model object. More info available from Prophet’s page

#Function to apply prophet model to timeseries
prophet_apply <- function(timeseries, growthtype = NULL) {
  if(is.null(growthtype))
     prophet(timeseries)
    else
      prophet(timeseries, growth = growthtype)
}

#Create future data_frame and predict on the model object
prophet_fcst_apply <-
  function(m,
           length_time,
           cap_size = NULL) {
    if (is.null(cap_size))
    { future_df <- make_future_dataframe(m, periods = length_time)
    }
    else 
    { future_df <- make_future_dataframe(m, periods = length_time)
      future_df['cap'] = cap_size
    }
    
  fcst_df <- predict(m, future_df)
  }

Model and forecast with prophet:

model_daily <- prophet_apply(daily_data)

## Initial log joint probability = -46.2524
## Optimization terminated normally: 
##   Convergence detected: relative gradient magnitude is below tolerance

model_daily_wgrowth <- prophet_apply(daily_Data_wgrowth, 'logistic')

## Initial log joint probability = -13.2458
## Optimization terminated normally: 
##   Convergence detected: relative gradient magnitude is below tolerance

Fcst_daily <- prophet_fcst_apply(model_daily, 730)
Fcst_daily_wgrowth <- prophet_fcst_apply(model_daily_wgrowth, 730, 7)

View forecasted units with their upper/lower confidence interval

#Select forecast with lower/upper confidence intervals from the predicted object
#Specify time frame for selection
view_select_Fcst <- function(fcst_df, date_begin, date_end) {
  selected_Fcst <- fcst_df %>% 
    filter(ds >date_begin  & ds< date_end) %>% 
    select(ds, yhat, yhat_lower, yhat_upper)
}

tail(view_select_Fcst(Fcst_daily, "2017-04-01", "2018-04-01"))

##             ds     yhat yhat_lower yhat_upper
## 360 2018-03-27 5.568770  1.2557720   9.688349
## 361 2018-03-28 5.449173  1.1129391   9.736892
## 362 2018-03-29 5.286332  0.9718378   9.680816
## 363 2018-03-30 5.475638  1.5285363   9.935465
## 364 2018-03-31 4.480532  0.3557986   8.664323
## 365 2018-04-01 5.195860  1.3188466   9.543473

Visualize the forecast by calling the generic plot function. I’m wrapping ggplotly(via Plotly package) around the plot function for interactive web-based version.

Plots for forecasted daily data:

#Plot function for daily fcst
plot_daily <- function(m, fcst, fnc) {
    fnc(m, fcst)
}

ggplotly(plot_daily(model_daily, Fcst_daily, plot))

plot_daily(model_daily, Fcst_daily, prophet_plot_components)

Sum forecast unit totals and forecast order dollars based on user specified price (in this case. price is set at $25).

#summarise yearly forecast units and order dollars
summary_fcst_units_price <- function(df, price, fcst_num) {
  df %>% 
   dplyr::summarise(Fcst_qty = sum(df[[fcst_num]]), Fcst_Dlrs = Fcst_qty*price)
}

Daily data set:

#Call summary_fcst_units_price function on the predicted daily numbers
sum_daily <- summary_fcst_units_price(view_select_Fcst(Fcst_daily, "2017-04-01", "2018-04-01"), 25, "yhat")
sum_daily

##   Fcst_qty Fcst_Dlrs
## 1 2022.837  50570.94

Plots for daily_data with growth

ggplotly(plot_daily(model_daily_wgrowth, Fcst_daily_wgrowth, plot))

plot_daily(model_daily_wgrowth, Fcst_daily_wgrowth, prophet_plot_components)

Daily_data with growth set:

tail(view_select_Fcst(Fcst_daily_wgrowth, "2017-04-01", "2018-04-01"))

##             ds     yhat yhat_lower yhat_upper
## 360 2018-03-27 6.733838   2.182734   11.12016
## 361 2018-03-28 6.599399   2.431310   11.28659
## 362 2018-03-29 6.510695   2.053849   11.02729
## 363 2018-03-30 6.648348   1.935214   11.06018
## 364 2018-03-31 7.842190   3.437448   11.95472
## 365 2018-04-01 7.684945   3.518858   11.78566

sum_daily_wgrowth <- summary_fcst_units_price(view_select_Fcst(Fcst_daily_wgrowth,  "2017-04-01", "2018-04-01"),25, "yhat")
sum_daily_wgrowth

##   Fcst_qty Fcst_Dlrs
## 1 2548.958  63723.95

#Auto ETS forecast
daily_ts <- ts(daily_data[,1], start(2016,1,1), frequency = 7)
daily_auto_fcst <- forecast(daily_ts, h = 365)
#autoplot(daily_auto_fcst)
ggplotly(autoplot(daily_auto_fcst))

sum_hyndman_ets <- summary_fcst_units_price(data.frame(daily_auto_fcst), 25, "Point.Forecast")

#Auto Arima Forecast
fit_ar_daily<- auto.arima(daily_ts)
daily_auto_ar_fcst <- forecast(fit_ar_daily, h = 365)
#autoplot(daily_auto_fcst)
ggplotly(autoplot(daily_auto_fcst))

sum_hyndman_ar <- summary_fcst_units_price(data.frame(daily_auto_ar_fcst), 25, "Point.Forecast")

All_TS_fcst <- full_join(full_join(sum_daily, sum_daily_wgrowth), full_join(sum_hyndman_ets, sum_hyndman_ar))
rownames(All_TS_fcst) <- c("Fcst_daily_prophet", "Fcst_daily_wgrowth_prophet", "Fcst_daily_forecast_ETS", "Fcst_daily_forecast_ARIMA")
knitr::kable(All_TS_fcst, caption = "Forecasts from Prophet & Forecast Package")