Time-series forecasting enables us to predict likely future values for a dataset based on historical time-series data. Time-series data collectively represents how a system, process, or behavior changes over time. When we accumulate millions of data points over a time period, we can build models to predict the next set of values likely to occur.
Time-series predictions can be used to:
Time-series forecasting alone is a powerful tool. But time-series data joined with business data can be a competitive advantage for any developer. TimescaleDB is PostgreSQL for time-series data and as such, time-series data stored in TimescaleDB can be easily joined with business data in another relational database in order to develop an even more insightful forecast into how your data (and business) will change over time.
In this time-series forecasting example, we will demonstrate how to integrate TimescaleDB with R, Apache MADlib, and Python to perform various time-series forecasting methods. We will be using New York City taxicab data that is also used in our Hello Timescale Tutorial. The dataset contains information about all yellow cab trips in New York City in January 2016, including pickup and dropoff times, GPS coordinates, and total price of a trip. We seek to extract some interesting insights from this rich dataset, build a time-series forecasting model, as well as explore the use of various forecasting and machine learning tools.
First, let's create our schema and populate our tables. Download the file
forecast.sql and execute the following command:
psql -U postgres -d nyc_data -h localhost -f forecast.sql
forecast.sql file contains SQL statements that create three
Let's look at how we create the
rides_count table as an example.
Here is a portion of the code taken from
CREATE TABLE rides_count( one_hour TIMESTAMP WITHOUT TIME ZONE NOT NULL, count NUMERIC ); SELECT create_hypertable('rides_count', 'one_hour'); INSERT INTO rides_count SELECT time_bucket_gapfill('1 hour', pickup_datetime, '2016-01-01 00:00:00','2016-01-31 23:59:59') AS one_hour, COUNT(*) AS count FROM rides WHERE ST_Distance(pickup_geom, ST_Transform(ST_SetSRID(ST_MakePoint(-74.0113,40.7075),4326),2163)) < 400 AND pickup_datetime < '2016-02-01' GROUP BY one_hour ORDER BY one_hour;
Notice that we have made the
rides_count table a TimescaleDB hypertable.
This allows us to take advantage of TimescaleDB's faster insert and query
performance with time-series data. Here, you can see how PostgreSQL aggregate
functions such as
COUNT and various PostGIS functions all work as usual
with TimescaleDB. We are using PostGIS to select data points from the original
rides table where the pickup location is less than 400m from the GPS location
(40.7589, -73.9851), which is Times Square.
Our data, supplied by the NYC Taxi and Limousine Commission, like most data,
is not perfect; it is missing data points for certain hours. We fill in the
missing values with 0, following the documentation that we have on
gap filling. An adaptation of the same method is used to achieve
the same result when creating
Before you move onto the next few sections, check that the following tables are in your database.
\dt List of relations Schema | Name | Type | Owner --------+-----------------+-------+---------- public | payment_types | table | postgres public | rates | table | postgres public | rides | table | postgres public | rides_count | table | postgres public | rides_length | table | postgres public | rides_price | table | postgres public | spatial_ref_sys | table | postgres (7 rows)
The ARIMA (Autoregressive Integrated Moving Average) model is a tool that is often used in time-series analysis to better understand a dataset and make predictions on future values. The ARIMA model can be broadly categorized as seasonal and non-seasonal. Seasonal ARIMA models are used for datasets that have characteristics that repeat over fixed periods of time. For example, a dataset of hourly temperature values over a week has a seasonal component with a period of 1 day, since the temperature goes up during the day and down over night every day. In contrast, the price of Bitcoin over time is (probably) non-seasonal since there is no clear observable pattern that recurs in fixed time periods.
We will be using R to analyze the seasonality of the number of taxicab pickups at Times Square over a week.
rides_count contains the data needed for this section of the tutorial.
rides_count has two columns
one_hour column is
time_bucket for every hour from January 1st to January 31st.
count column is the number of pickups from Times Square during each hourly period.
SELECT * FROM rides_count; one_hour | count ---------------------+------- 2016-01-01 00:00:00 | 176 2016-01-01 01:00:00 | 218 2016-01-01 02:00:00 | 221 2016-01-01 03:00:00 | 344 2016-01-01 04:00:00 | 397 2016-01-01 05:00:00 | 269 2016-01-01 06:00:00 | 192 2016-01-01 07:00:00 | 145 2016-01-01 08:00:00 | 166 2016-01-01 09:00:00 | 233 2016-01-01 10:00:00 | 295 2016-01-01 11:00:00 | 440 2016-01-01 12:00:00 | 472 2016-01-01 13:00:00 | 472 2016-01-01 14:00:00 | 485 2016-01-01 15:00:00 | 538 2016-01-01 16:00:00 | 430 2016-01-01 17:00:00 | 451 2016-01-01 18:00:00 | 496 2016-01-01 19:00:00 | 538 2016-01-01 20:00:00 | 485 2016-01-01 21:00:00 | 619 2016-01-01 22:00:00 | 1197 2016-01-01 23:00:00 | 798 ...
We will create two PostgreSQL views,
the training and testing datasets.
-- Make the training dataset CREATE VIEW rides_count_train AS SELECT * FROM rides_count WHERE one_hour <= '2016-01-21 23:59:59'; -- Make the testing dataset CREATE VIEW rides_count_test AS SELECT * FROM rides_count WHERE one_hour >= '2016-01-22 00:00:00';
R has an RPostgres package which allows you to connect to your database from R.
The code below establishes a connection to the PostgreSQL database
You can connect to a different database simply by changing the parameters of
dbConnect. The final line of code should print out a list of all tables in
your database. This means that you have successfully connected and are ready
to query the database from R.
# Install and load RPostgres package install.packages("RPostgres") library("DBI") # creates a connection to the postgres database con <- dbConnect(RPostgres::Postgres(), dbname = "nyc_data", host = "localhost", user = "postgres") # list tables in database to verify connection dbListTables(con)
We can query the database with SQL code inside R. Putting the query result in an R data frame allows us to analyze the data using tools provided by R.
# query the database and input the result into an R data frame # training dataset with data 2016/01/01 - 2016/01/21 count_rides_train_query <- dbSendQuery(con, "SELECT * FROM rides_count_train;") count_rides_train <- dbFetch(count_rides_train_query) dbClearResult(count_rides_train_query) head(count_rides_train) one_hour count 1 2016-01-01 00:00:00 176 2 2016-01-01 01:00:00 218 3 2016-01-01 02:00:00 221 4 2016-01-01 03:00:00 344 5 2016-01-01 04:00:00 397 6 2016-01-01 05:00:00 269 # testing dataset with data 2016/01/22 - 2016/01/31 count_rides_test_query <- dbSendQuery(con, "SELECT * FROM rides_count_test") count_rides_test <- dbFetch(count_rides_test_query) dbClearResult(count_rides_test_query) head(count_rides_test) one_hour count 1 2016-01-22 00:00:00 702 2 2016-01-22 01:00:00 401 3 2016-01-22 02:00:00 247 4 2016-01-22 03:00:00 169 5 2016-01-22 04:00:00 140 6 2016-01-22 05:00:00 100
In order to feed the data into an ARIMA model, we must first convert the
data frame into a time-series object in R.
xts is a package that allows
us to do this easily. We also set the frequency of the time-series object
to 168. This is because we expect the number of pickups to fluctuate with
a fixed pattern every week, and there are 168 hours in a week, or in other
words, 168 data points in each seasonal period. If we wanted to model
the data as having a seasonality of 1 day, we can change the frequency
parameter to 24.
# Install and load xts package install.packages("xts") library("xts") # convert the data frame into time-series xts_count_rides <- xts(count_rides_train$count, order.by = as.POSIXct(count_rides_train$one_hour, format = "%Y-%m-%d %H:%M:%S")) # set the frequency of series as weekly 24 * 7 attr(xts_count_rides, 'frequency') <- 168
forecast package in R provides a useful function
which automatically finds the best ARIMA parameters for the dataset.
The parameter D, which captures the seasonality of the model, is set
to 1 to force the function to find a seasonal model. Note that this
calculation can take a while to compute (in this dataset, around 5 minutes).
Once the computation is complete, we save the output of the
fit and get a summary of the ARIMA model that has been created.
# Install and load the forecast package needed for ARIMA install.packages("forecast") library("forecast") # use auto.arima to automatically get the arima model parameters with best fit fit <- auto.arima(xts_count_rides[,1], D = 1, seasonal = TRUE) # see the summary of the fit summary(fit) Series: xts_count_rides[, 1] ARIMA(4,0,2)(0,1,0) with drift Coefficients: ar1 ar2 ar3 ar4 ma1 ma2 drift 2.3211 -1.8758 0.3959 0.1001 -1.7643 0.9444 0.3561 s.e. 0.0634 0.1487 0.1460 0.0588 0.0361 0.0307 0.0705 sigma^2 estimated as 5193: log likelihood=-1911.21 AIC=3838.42 AICc=3838.86 BIC=3868.95 Training set error measures: ME RMSE MAE MPE MAPE MASE Training set -0.2800571 58.22306 33.15943 -1.783649 7.868031 0.4257707 ACF1 Training set -0.02641353
Finally, the ARIMA model can be used to forecast future values.
h parameter specifies the number of steps we want to forecast.
# forecast future values using the arima model, h specifies the number of readings to forecast fcast <- forecast(fit, h=168) fcast Point Forecast Lo 80 Hi 80 Lo 95 Hi 95 4.000000 659.0645 566.71202 751.4169 517.82358229 800.3053 4.005952 430.7339 325.02891 536.4388 269.07209741 592.3956 4.011905 268.1259 157.28358 378.9682 98.60719504 437.6446 4.017857 228.3024 116.08381 340.5210 56.67886523 399.9260 4.023810 200.7340 88.25064 313.2174 28.70554423 372.7625 4.029762 140.5758 28.04128 253.1103 -31.53088134 312.6824 4.035714 196.1703 83.57555 308.7650 23.97150358 368.3690 4.041667 282.6171 169.80545 395.4288 110.08657346 455.1476 4.047619 446.6713 333.28115 560.0614 273.25604289 620.0865 4.053571 479.9449 365.53618 594.3537 304.97184340 654.9180 ...
The output of
forecast can be hard to decipher. You can plot the
forecasted values with the code below:
# plot the values forecasted plot(fcast, include = 168, main="Taxicab Pickup Count in Times Square by Time", xlab="Date", ylab="Pickup Count", xaxt="n", col="red", fcol="blue") ticks <- seq(3, 5, 1/7) dates <- seq(as.Date("2016-01-15"), as.Date("2016-01-29"), by="days") dates <- format(dates, "%m-%d %H:%M") axis(1, at=ticks, labels=dates) legend('topleft', legend=c("Observed Value", "Predicted Value"), col=c("red", "blue"), lwd=c(2.5,2.5)) # plot the observed values from the testing dataset count_rides_test$x <- seq(4, 4 + 239 * 1/168, 1/168) count_rides_test <- subset(count_rides_test, count_rides_test$one_hour < as.POSIXct("2016-01-29")) lines(count_rides_test$x, count_rides_test$count, col="red")
In our graphing of this data, the grey area around the prediction line in blue is the prediction interval, i.e. the uncertainty of the prediction, while the red line is the actual observed pickup count.The number of pickups on Saturday January 23rd is zero because the data is missing for this period of time.
We find that the prediction for January 22nd matches impressively with the observed values, but the prediction overestimates for the following days. It is clear that the model has captured the seasonality of the data, as you can see the forecasted values of the number of pickups drop dramatically overnight from 1am, before rising again from around 6am. There is a noticeable increase in the number of pickups in the afternoon compared to the morning, with a slight dip around lunchtime and a sharp peak around 6pm when presumably people take cabs to return home after work.
While these findings do not reveal anything completely unexpected, it is still valuable to have the analysis verify our expectations. It must be noted that the ARIMA model is not perfect and this is evident from the anomalous prediction made for January 25th. The ARIMA model created uses the previous week's data to make predictions. January 18th 2016 was Martin Luther King day, and so the distribution of ride pickups throughout the day is slightly different from that of a standard Monday. Also, the holiday probably affected riders' behavior on the surrounding days too. The model does not pick up such anomalous data that arise from various holidays and this must be noted before reaching a conclusion. Simply taking out such anomalous data, by only using the first two weeks of January for example, may have led to a more accurate prediction. This demonstrates the importance of understanding the context behind our data.
Although R offers a rich library of statistical models, we had to import the data into R before performing calculations. With a larger dataset, this can become a bottleneck to marshal and transfer all the data to the R process (which itself might run out of memory and start swapping). So, we will now look into an alternative method that allows us to move our computations to the database and improve this performance.
MADlib is an open-source library for in-database data analytics that provides a wide collection of popular machine learning methods and various supplementary statistical tools.
MADlib supports many machine learning algorithms that are available in R and Python. And by executing these machine learning algorithms within the database, it may be efficient enough to process them against an entire dataset rather than pulling a much smaller sample to an external program.
Install MADlib following the steps outlined in their documentation: MADlib Installation Guide.
Set up MADlib in our
/usr/local/madlib/bin/madpack -s madlib -p postgres -c [email protected]/nyc_data install
Now we can make use of MADlib's library to analyze our taxicab dataset. Here, we will train an ARIMA model to predict the price of a ride from JFK to Times Square at a given time.
Let's look at the
rides_price table. The
trip_price column is
the the average price of a trip from JFK to Times Square during
each hourly period. Data points that are missing due to no rides
being taken during a certain hourly period are filled with the
previous value. This is done by gap filling,
mentioned earlier in this tutorial.
SELECT * FROM rides_price; one_hour | trip_price ---------------------+------------------ 2016-01-01 00:00:00 | 58.34 2016-01-01 01:00:00 | 58.34 2016-01-01 02:00:00 | 58.34 2016-01-01 03:00:00 | 58.34 2016-01-01 04:00:00 | 58.34 2016-01-01 05:00:00 | 59.59 2016-01-01 06:00:00 | 58.34 2016-01-01 07:00:00 | 60.3833333333333 2016-01-01 08:00:00 | 61.2575 2016-01-01 09:00:00 | 58.435 2016-01-01 10:00:00 | 63.952 2016-01-01 11:00:00 | 59.9576923076923 2016-01-01 12:00:00 | 60.462 2016-01-01 13:00:00 | 61.65 2016-01-01 14:00:00 | 58.342 2016-01-01 15:00:00 | 59.8965 2016-01-01 16:00:00 | 61.6468965517241 2016-01-01 17:00:00 | 58.982 2016-01-01 18:00:00 | 64.28875 2016-01-01 19:00:00 | 60.8433333333333 2016-01-01 20:00:00 | 61.888125 2016-01-01 21:00:00 | 61.4064285714286 2016-01-01 22:00:00 | 61.107619047619 2016-01-01 23:00:00 | 57.9088888888889
We will also create two tables for the training and testing datasets. We create tables instead of views here because we need to add columns to these datasets later in our time-series forecast analysis.
-- Make the training dataset SELECT * INTO rides_price_train FROM rides_price WHERE one_hour <= '2016-01-21 23:59:59'; -- Make the testing dataset SELECT * INTO rides_price_test FROM rides_price WHERE one_hour >= '2016-01-22 00:00:00';
Now we will use MADlib's ARIMA library to make forecasts on our dataset.
MADlib does not yet offer a method that automatically finds the best
parameters of the ARIMA model. So, the non-seasonal orders of our
ARIMA model is obtained by using R's
auto.arima function in the same
way we obtained them in the previous section with seasonal ARIMA.
Here is the R code:
# Connect to database and fetch records library("DBI") con <- dbConnect(RPostgres::Postgres(), dbname = "nyc_data", host = "localhost", user = "postgres") rides_price_train_query <- dbSendQuery(con, "SELECT * FROM rides_price_train;") rides_price_train <- dbFetch(rides_price_train_query) dbClearResult(rides_price_train_query) # convert the dataframe into a time-series library("xts") xts_rides_price <- xts(rides_price_train$trip_price, order.by = as.POSIXct(rides_price_train$one_hour, format = "%Y-%m-%d %H:%M:%S")) attr(xts_rides_price, 'frequency') <- 168 # use auto.arima() to calculate the orders library("forecast") fit <- auto.arima(xts_rides_price[,1]) # see the summary of the fit summary(fit) Series: xts_rides_price[, 1] ARIMA(2,1,3) Coefficients: ar1 ar2 ma1 ma2 ma3 0.3958 -0.5142 -1.1906 0.8263 -0.5791 s.e. 0.2312 0.1593 0.2202 0.2846 0.1130 sigma^2 estimated as 11.06: log likelihood=-1316.8 AIC=2645.59 AICc=2645.76 BIC=2670.92 Training set error measures: ME RMSE MAE MPE MAPE MASE Training set 0.1319955 3.30592 2.186295 -0.04371788 3.47929 0.6510487 ACF1 Training set -0.002262549
Of course, we could simply continue our analysis with R by following the same steps in the previous seasonal ARIMA section. Unfortunately, MADlib does not yet offer a way to automatically find the orders of the ARIMA model.
However with a larger dataset, you could take the approach of loading a subset of the data to calculate the model's parameters in R and then train the model using MADlib. You can use a combination of the options outlined in this tutorial to take advantage of the strengths and work around weaknesses of the different tools.
Using the parameters ARIMA(2,1,3) found using R, we will use MADlib's
-- train arima model and forecast the price of a ride from JFK to Times Square DROP TABLE IF EXISTS rides_price_output; DROP TABLE IF EXISTS rides_price_output_residual; DROP TABLE IF EXISTS rides_price_output_summary; DROP TABLE IF EXISTS rides_price_forecast_output; SELECT madlib.arima_train('rides_price_train', -- input table 'rides_price_output', -- output table 'one_hour', -- timestamp column 'trip_price', -- time-series column NULL, -- grouping columns TRUE, -- include_mean ARRAY[2,1,3] -- non-seasonal orders ); SELECT madlib.arima_forecast('rides_price_output', -- model table 'rides_price_forecast_output', -- output table 240 -- steps_ahead (10 days) );
Let's examine what values the trained ARIMA model forecasted for the next day.
SELECT * FROM rides_price_forecast_output; steps_ahead | forecast_value -------------+---------------- 1 | 62.3175746635 2 | 62.7126520845 3 | 62.8920386424 4 | 62.7550446339 5 | 62.606406819 6 | 62.6197088842 7 | 62.7032173055 8 | 62.7292577943 9 | 62.6956015822 10 | 62.6685763075 ...
The model seems to suggest that the price of a ride from JFK to Times Square remains pretty much constant on a day-to-day basis. MADlib also provides various statistical functions to evaluate the model.
ALTER TABLE rides_price_test ADD COLUMN id SERIAL PRIMARY KEY; ALTER TABLE rides_price_test ADD COLUMN forecast DOUBLE PRECISION; UPDATE rides_price_test SET forecast = rides_price_forecast_output.forecast_value FROM rides_price_forecast_output WHERE rides_price_test.id = rides_price_forecast_output.steps_ahead; SELECT madlib.mean_abs_perc_error('rides_price_test', 'rides_price_mean_abs_perc_error', 'trip_price', 'forecast'); SELECT * FROM rides_price_mean_abs_perc_error; mean_abs_perc_error --------------------- 0.0423789161532639 (1 row)
We had to set up the columns of the
rides_price_test table to
fit the format of MADlib's
mean_abs_perc_error function. There
are multiple ways to evaluate the quality of a model's forecast
values. In this case, we calculated the mean absolute percentage
error and got 4.24%.
What might we take away from this? Our non-seasonal ARIMA model predicts that the price of a trip from the airport to Manhattan remains constant at $62 and performs well against the testing dataset. Unlike some ride hailing apps such as Uber that have surge pricing during rush hours, yellow taxicab prices stay pretty much constant all day.
From a technical standpoint, we have seen how TimescaleDB integrates seamlessly with other PostgreSQL extensions PostGIS and MADlib. This means that TimescaleDB users can easily take advantage of the vast PostgreSQL ecosystem.
The Holt-Winters model is another widely used tool in time-series analysis and forecasting. It can only be used for seasonal time-series data. The Holt-Winters model uses simple exponential smoothing to make future predictions. So with time-series data, the forecast is calculated from taking a weighted average of past values, with more recent data points having greater weight than previous points. Holt-Winters is considered to be simpler than ARIMA, but there is no clear answer as to which time-series prediction model is superior in time-series forecasting. It is advised to create both models for a particular dataset and compare the performance to find out which is more suitable.
We will use Python to analyze how long it takes from the Financial District to Times Square at different time periods during the day. We need to install various Python packages:
pip install psycopg2 pip install pandas pip install numpy pip install statsmodels
The format of the data is very similar to the previous two sections.
trip_length column in the
rides_length table is the average
length of a ride from the Financial District to Times Square in the
given time period.
SELECT * FROM rides_length; three_hour | trip_length ---------------------+----------------- 2016-01-01 00:00:00 | 00:21:50.090909 2016-01-01 03:00:00 | 00:17:15.8 2016-01-01 06:00:00 | 00:13:21.666667 2016-01-01 09:00:00 | 00:14:20.625 2016-01-01 12:00:00 | 00:16:32.366667 2016-01-01 15:00:00 | 00:19:16.921569 2016-01-01 18:00:00 | 00:22:46.5 2016-01-01 21:00:00 | 00:17:22.285714 2016-01-02 00:00:00 | 00:19:24 2016-01-02 03:00:00 | 00:19:24 2016-01-02 06:00:00 | 00:12:13.5 2016-01-02 09:00:00 | 00:17:17.785714 2016-01-02 12:00:00 | 00:20:56.785714 2016-01-02 15:00:00 | 00:24:41.730769 2016-01-02 18:00:00 | 00:29:39.555556 2016-01-02 21:00:00 | 00:20:09.6 ...
We will also create two PostgreSQL views for the training and testing datasets.
-- Make the training dataset CREATE VIEW rides_length_train AS SELECT * FROM rides_length WHERE three_hour <= '2016-01-21 23:59:59'; -- Make the testing dataset CREATE VIEW rides_length_test AS SELECT * FROM rides_length WHERE three_hour >= '2016-01-22 00:00:00';
Python has a
psycopg2 package that allows you to query the
database in Python:
import psycopg2 import psycopg2.extras # establish connection conn = psycopg2.connect(dbname='nyc_data', user='postgres', host='localhost') # cursor object allows querying of database # server-side cursor is created to prevent records to be downloaded until explicitly fetched cursor_train = conn.cursor('train', cursor_factory=psycopg2.extras.DictCursor) cursor_test = conn.cursor('test', cursor_factory=psycopg2.extras.DictCursor) # execute SQL query cursor_train.execute('SELECT * FROM rides_length_train') cursor_test.execute('SELECT * FROM rides_length_test') # fetch records from database ride_length_train = cursor_train.fetchall() ride_length_test = cursor_test.fetchall()
We now manipulate the data to feed it into the Holt-Winters model.
import pandas as pd import numpy as np # make records into a pandas dataframe ride_length_train = pd.DataFrame(np.array(ride_length_train), columns = ['time', 'trip_length']) ride_length_test = pd.DataFrame(np.array(ride_length_test), columns = ['time', 'trip_length']) # convert the type of columns of dataframe to datetime and timedelta ride_length_train['time'] = pd.to_datetime(ride_length_train['time'], format = '%Y-%m-%d %H:%M:%S') ride_length_test['time'] = pd.to_datetime(ride_length_test['time'], format = '%Y-%m-%d %H:%M:%S') ride_length_train['trip_length'] = pd.to_timedelta(ride_length_train['trip_length']) ride_length_test['trip_length'] = pd.to_timedelta(ride_length_test['trip_length']) # set the index of dataframes to the timestamp ride_length_train.set_index('time', inplace = True) ride_length_test.set_index('time', inplace = True) # convert trip_length into a numeric value in seconds ride_length_train['trip_length'] = ride_length_train['trip_length']/np.timedelta64(1, 's') ride_length_test['trip_length'] = ride_length_test['trip_length']/np.timedelta64(1, 's')
This data can now be used to train a Holt-Winters model that
is imported from the
statsmodels package. We expect a pattern
to repeat weekly, and therefore set the
parameter to 56 (there are eight 3-hour periods in a day,
seven days in a week). Since we expect the seasonal variations
to be fairly constant over time, we use the additive method rather
than the multiplicative method, which is specified by the
from statsmodels.tsa.api import ExponentialSmoothing fit = ExponentialSmoothing(np.asarray(ride_length_train['trip_length']), seasonal_periods = 56, trend = 'add', seasonal = 'add').fit()
We use the model that has been trained to make a forecast and compare with the testing dataset.
ride_length_test['forecast'] = fit.forecast(len(ride_length_test))
ride_length_test has a column with the observed values and
predicted values from January 22nd to January 31st. We can plot
these values on top of each other to make a visual comparison:
import matplotlib.pyplot as plt plt.plot(ride_length_test) plt.title('Taxicab Ride Length from Financial District to Times Square by Time') plt.xlabel('Date') plt.ylabel('Ride Length (seconds)') plt.legend(['Observed', 'Predicted']) plt.show()
The model predicts that the length of a trip from the Financial District to Times Square fluctuates roughly between 16 minutes and 38 minutes, with high points midday and low points overnight. The trip length is notably longer during weekdays than it is during weekends (January 23rd 24th, 30th, 31st).
The initial reaction from the plotted graph is that the model does a relatively good job in capturing the overall trend, but at times has quite a large margin of error. This can be due to the inherent irregularity of Manhattan's traffic situation with frequent roadblocks, accidents and unexpected weather conditions. Moreover, as it was the case with taxi pickup counts in our analysis with R using the seasonal ARIMA model, the Holt-Winters model was also thrown off by the anomalous data points on Martin Luther King day on the previous Monday.
We looked at different ways you can build statistical models to analyze time-series data and how you can leverage the full power of the PostgreSQL ecosystem with TimescaleDB. In this tutorial we looked at integrating TimescaleDB with R, Apache MADlib, and Python. You can simply choose the option you are most familiar with from a vast number of choices that TimescaleDB inherits from PostgreSQL. ARIMA and Holt-Winters are just a couple from a wide variety of statistical models and machine learning algorithms that you can use to analyze and make predictions on time-series data in your TimescaleDB database.
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