README.md

In placeboo/amplify: Forecasting Daily Time Seriers with Double Seasonal Patterns

Amplify Package: Double seasonal daily time series (Update 0.2.0)

Jiaqi (Jackie) Yin 09/15/2020

• Install R package
• Smoothing
• Validation
• Prediction
• Holiday Modification

I have leveraged more features to the Amplify Package. Now we release the updated version 0.2.0. The latest one update functions modify_pred, smooth_ts. find_adj_date, and select_model. For the first three functions, I have added a mode called weekday.sep = FALSE. If the weekday.sep = TRUE, one of the seasonal pattern is weekly and time series is implemented respectively according to their weekdays. In select_model, I have added cross validation option. See more details below.

Our package is for double seasonal daily time seriers. Data features include outliers, variation increasing/decreasing, and double seasonality. We build multiplicative modeling for time series.

In this document, we explain how to use our R package.

To showing the steps, we forecast the some airline supporting tickets for FY20 as an example.

Install R package

Install the package from github

devtools::install_github("placeboo/amplify", force = TRUE)

We start from loading our package Amplify.

library(amplify)

We have support ticket from 2014-07-01 to 2018-06-10. A glimpse of the data:

| date | ticket | | :--------- | -----: | | 2014-07-01 | 4540 | | 2014-07-02 | 4547 | | 2014-07-03 | 3888 | | 2014-07-04 | 2172 | | 2014-07-05 | 435 | | 2014-07-06 | 486 | | 2014-07-07 | 4411 | | 2014-07-08 | 4475 | | 2014-07-09 | 4183 |

In the package, we have a holiday data set. For forecasting, you can add your own holiday information. It should include the date and the name of the holidays. Have a look:

data("holiday")
head(holiday)

| date | name | is\_holiday | | :--------- | :---------------------- | :----------- | | 2014-01-01 | NewYear | Yes | | 2014-01-02 | AfterNewYear1 | AfterHoliday | | 2014-01-03 | AfterNewYear2 | AfterHoliday | | 2014-01-20 | Martin Luther King Day | Yes | | 2014-02-11 | National Foundation Day | Yes | | 2014-03-01 | Carnival Saturday | Yes |

Smoothing

The whole data set is our training set. We aim to predict the daily tickets from 2019-07-01 to 2020-06-30. First we detect the outiers and impute them with reasonable value.

smooth.ls = smooth_ts(data = tickets,
                      vars = c("date", "ticket"),
                      par = list(lambda = 1.5, s = 7),
                      weekday.sep = TRUE)

train.dat = cbind(tickets, smooth.ls$ts.dat)
head(train.dat) 

| date | ticket | is\_outlier | ts | | :--------- | -----: | :---------- | -------: | | 2014-07-01 | 4540 | no | 4540.000 | | 2014-07-02 | 4547 | no | 4547.000 | | 2014-07-03 | 3888 | no | 3888.000 | | 2014-07-04 | 2172 | yes | 3437.725 | | 2014-07-05 | 435 | no | 435.000 | | 2014-07-06 | 486 | no | 486.000 |

Validation

We split the data set into subtraining set and validation set to find parameters. There are 5 parameters ({\alpha, \beta, \gamma, \omega, \phi }) in the model. We use grid search to find a set of optimal parameters. The searching process has been optimized by parallel computing. We also implement cross validation.

train.start = 20140701
train.end = 20190630

subtrain.end = 20190430
valid.start = 20190501

valid.ls = train_test_split(train.dat,
                            train.window = c(train.start, subtrain.end),
                            test.window = c(valid.start, train.end))

subtrain.dat = valid.ls$train.dat
valid.dat = valid.ls$test.dat

tic("grid search")
select.ls = select_model(train.y = subtrain.dat$ts,
                         valid.y = valid.dat$ts,
                         grid.search = TRUE,
                         search.length = c(-0.5, 0.5), 
                         length.out = 5,
                         CV = TRUE,
                         kfold = 4)
toc()

## grid search: 206.84 sec elapsed

The list select.ls contains the model which has the smallest MAPE for validation set, and the validation results.

cv = select.ls$cv
head(cv) 

| alpha | beta | gamma | omega | phi | me | rmse | mpe | mape | | --------: | -------: | --------: | --------: | --------: | -------: | -------: | --------: | --------: | | 0.0413436 | 2.35e-05 | 0.0319544 | 0.1558890 | 0.0011155 | 144.2273 | 357.7416 | 0.0184198 | 0.0400901 | | 0.0206718 | 1.18e-05 | 0.0159772 | 0.0779445 | 0.0005577 | 187.4765 | 397.0671 | 0.0202587 | 0.0460451 | | 0.0206718 | 1.18e-05 | 0.0159772 | 0.0779445 | 0.0008366 | 187.4774 | 397.0681 | 0.0202588 | 0.0460452 | | 0.0206718 | 1.18e-05 | 0.0159772 | 0.0779445 | 0.0011155 | 187.4784 | 397.0691 | 0.0202589 | 0.0460453 | | 0.0206718 | 1.18e-05 | 0.0159772 | 0.0779445 | 0.0013943 | 187.4793 | 397.0701 | 0.0202590 | 0.0460454 | | 0.0206718 | 1.18e-05 | 0.0159772 | 0.0779445 | 0.0016732 | 187.4803 | 397.0711 | 0.0202591 | 0.0460455 |

We pick the parameters which yield the lowest MAPE.

cv[which.min(cv$mape), ]

| | alpha | beta | gamma | omega | phi | me | rmse | mpe | mape | | ---- | --------: | -------: | --------: | --------: | --------: | -------: | -------: | --------: | --------: | | 1872 | 0.0413436 | 3.53e-05 | 0.0479317 | 0.2338336 | 0.0005577 | 138.4206 | 347.6489 | 0.0215749 | 0.0380518 |

Prediction

We first build a future data frame

pred.dat = build_date(20190701, 20200630)
head(pred.dat) 

| date | | :--------- | | 2019-07-01 | | 2019-07-02 | | 2019-07-03 | | 2019-07-04 | | 2019-07-05 | | 2019-07-06 |

Within the data frame, we fill the predicted tickets.

model = select.ls$model

pred.ls = forecast(model, h = nrow(pred.dat))
pred = as.numeric(pred.ls$mean)
pred.dat = pred.dat %>%
  mutate(pred = pred)

head(pred.dat) 

| date | pred | | :--------- | -------: | | 2019-07-01 | 8939.624 | | 2019-07-02 | 9699.908 | | 2019-07-03 | 9506.293 | | 2019-07-04 | 9297.721 | | 2019-07-05 | 7869.112 | | 2019-07-06 | 1192.328 |

Holiday Modification

We define the distance between the actual and predictiona and then adjust the holidays.

tmp = cbind(train.dat, pred = as.numeric(fitted(model)))
tmp = tmp %>%
  mutate(resid = (ticket - pred) / pred)

In order to capture floating holidays such as Easter, we add more information about Holidays.

modify.ls = modify_pred(tmp,
                        vars = c("date", "resid"),
                        time.window = c(20190701, 20200630),
                        par = list(lambda = 1.5, n = 3), 
                        holiday = holiday)

h.hat =  modify.ls$h.mat$h.hat
h.hat[h.hat > 0] = 0
pred.dat = pred.dat %>%
  mutate(h.hat = h.hat,
         pred_modify = pred * (1 + h.hat))

pred.dat %>%
  ggplot(aes(x = date, y = pred_modify)) +
  geom_point(size = 2, alpha = 0.6) + 
  geom_line() +
  scale_x_date(name = "Date",
                date_breaks = "1 month") + 
  ylab("Tickets") + 
  theme(axis.text.x = element_text(angle = 30, hjust = 1))

placeboo/amplify documentation built on Oct. 6, 2020, 9:04 a.m.