This report centralizes the findings of the analysis and modelling of a small dataset or panel, of about 2M taxi ride trips, in period of 122 days.
It describes the story of analysing the data, creating a timeseries of trips per hour and then attempts to model and predict the future with comon timeseries analysis techniques.
It was written in a short timeframe and acts as the overeview of the project.
Much like a table of contents.
The meat of the project lies in the
5 Jupyter Notebooks in the notebooks/ folder.
Taxi ride analysis is an important metric for a company working in the field. Even more so for hourly trip count forecasting, which is chosen as our analysis centerpoint.
The project is an installable package, and organized to help a future analyst reproduce and extend the results. It was based on:
https://drivendata.github.io/cookiecutter-data-science/
Take a look at README.md for a quick tour, installation and usage instuctions.
The detailed analysis lives in the 5 notebooks under /notebooks and we'll
get into it right away.
The data was first explored and cleaned during the first two notebooks.
Numbers on headers represent the relevant notebooks.
Pandas is used throughout the analysis as the container type of choice for our dataset and timeseries data.
NaN values were dropped as they were but a small percentage (<<0.01) of the data.
First the columns source_latitude, source_longitude and equivalent two destination
columns were explored.
Starting with a quick boxplot and histogram to find out the std, mean and variance,
helps to start thinking about possible outliers. Quick scatterplots and use of
maps with folium (https://python-visualization.github.io/folium/) helped to
make sure, in a quick and dirty way, that trips were on land and at the right city.
After making sure there were not many trips outside the city, the next thing was to do the same boxplot and histogram for trip counts per day.
The data spawned for about 122 days.
Passenger id's were a problem to decipher, as some id's would conduct thousands of trips from and to specific addresses, without necessarily going back.
It was concluded that these id's have some special quality, for which the context is missing, and is no use getting much into.
The feature was created introduced to the dataset and explored with the same methods (boxplot, histogram) as the rest.
There was no time, but a correlation matrix between dataset features was in order at this point.
This next notebook removed outliers which were under 0.5% and over 99.5%
of the range of all numerical values: lat, lon, distance and trip_counts
per hour.
Then after switching gear to the timeseries depicting trip-counts-per-hour,
a deliberate graphical exploration revealed the general trend and 2 most
prevalent seasonalities of the dataset.
This part goes through the ideas of stationality on a dataset and introduces the basic tests to clear that notion.
Furthermore, autocorrelation and frequency graphs help give an idea of the complexity inherent in the timeseries.
After preparing a simple train-test split, an automatic grid search algorithm was used to determine the three key values for ARIMA.
Choosing the train test split to the unorthodox 99% - 1% happened so as to try to allow the model to adjust to the extreme trend changes in that final week.
As a standard process forecasts are evaluated in and out of sample with the use of a graph. Time did not allow for cross validation for in-sample-predictions. Then the standardized residual is also evaluated in a qualitative manner.
The residuals showed that further information was preserved in them, but that happened most of the time. A qualititive look of the graph revealed that out of sample predictions did not contained no seasonality whatsoever.
RMSE is used as a metric for out-of-sample predictions. The value was not judged as too bad, considering the scale of values:
- Test RMSE: 545.974
Next we explore the idea of forecasting seasonality along with trend, using an automated grid search model trainer, to chose the extra parameters for a proper SARIMA model forecasting. We allow seasonality to go as far as 24, for computational ease.
Complicated SARIMA models, along with different parameter testing, lead to long training times.
The standard procedure of qualitative evaluation through graphs is followed again, and RMSE is used as the numeric metric for out-of-sample predictions once again.
Residual plots, were worse than the naive approach and although the out-of-sample predictions contain strong evidence of seasonality, the RMSE score doubled.
- Test RMSE: 1009.208
On the other hand, the out-of-sample prediction had managed to model the 24-hour season cycles we asked for it to model.
Deseasoning is the process of removing seasonality components from a timeseries, allowing only for the trend to remain.
As we already are aware from our preliminary exploration, that the data have 2 strong 24h and 7d seasonalities embedded in them. The multiplicative method of deseasoning was preferred, as it was noticed that freq variations increased in amplitude, when the trend did the same.
Two consecutive deseasoning operations allow for a clearer form of the trend line, and we try to model it using a very simple auto-ARIMA model, with minimum seasonality.
Moreover, the fitting time has reduced significantly.
Evaluating the plot diagnostics of the standardized residuals, did not show much of an improvement, but out-of-sample RMSE dropped a further.
- Test RMSE: 183.112
It is worth reminding at this point, that this value was for the mere trend of the timeseries, after removing the 2 seasonality components.
Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, and daily seasonality, plus holiday effects. It works best with time series that have strong seasonal effects and several seasons of historical data.
Prophet is robust to missing data and shifts in the trend, and typically handles outliers well. Running Prophet on the raw data, with NaN's did not seem to make a big difference for the method.
Still the data was relatively clean to begin with, and the cleaned data was preferred for the final runs, so as to keep a golden standard throughout our experiments.
Cross validation was conducted in sample, showing an average of 1000 for RMSE, including some fluctuations.
The first run of Prophet, was with the basic settings. It the ease of use, combined with good results and intuitive looking plots, that made it stand out. Not only was Prophet accurate, but also much quicker than SARIMA to train. That allowed for more iterations, while ready to use tools allowed also for a cross validation of the model.
The final iteration with Prophet was more elaborate.
Qualities like use of logistic (instead of linear) growth and use multiplicative
(instead of additive) seasonality, to model both trend and seasonality allowed
for more room.
Quick experiments were made with model parameters to allow for more flexibility and changepoints for the trend. Prophet allows for setting up holidays, where the model is allowed to deviate a lot from it's trend, in order to support them.
So Christmas season and Christmas day were introduced as holidays, along with 14 Peruvian holidays, two of which occured during that period and excibit a spike in actual and modelled trip counts.
Moreover both 24h and 7d prevalent seasonalities were detected.
A floor of 0 was also stated, as it is impossible to have negative trips, and also a ceiling of 10000 trips per day. These two cuttoffs are respected by the model's trend and it does not surpass them.
You can see them as dashed lines in the first plot in this section.
Cross validation happened in-sample, where RMSE ranged around 1000, with less fluctuations that the basic model.
Validation periods were 5 days long, with 15 day intervals between them, starting only after the first 60 days of data.
In this analysis we showed several methods and tools that can help to model a timeseries. After the initial data exploration and outlier removal, ARIMA was introduced, as a naive and a SARIMA modelling tool, with interesting results.
Then we used decomposition to examine how ARIMA would model a cleaned up trend from it's strongest seasonality coefficients, and indeed that went well.
Finally we experimented with the Prophet model, which surprised with it's features, speed, ease of use and accuracy.