R; Time series analysis on sensor data

Question

I have a data frame of sensor data

I have a data frame as follows:

pressure    datetime
4.848374    2016-04-12 10:04:00   
4.683901    2016-04-12 10:04:32   
5.237860    2016-04-12 10:13:20 

Now, I would like to apply ARIMA to make predictive analytics.

Since the data is not sampled uniformly, I have aggregated it on Hourly basis which looks as follows:

datetime                    pressure
"2016-04-19 00:00:00 BST"   5.581806
"2016-04-19 01:00:00 BST"   4.769832
"2016-04-19 02:00:00 BST"   4.769832  
"2016-04-19 03:00:00 BST"   4.553711  
"2016-04-19 04:00:00 BST"   6.285599  
"2016-04-19 05:00:00 BST"   5.873414

The pressure for every hour looks like below:

But I can't create ts object as I am not sure what the frequency should be for Hourly data.

Answer 1

Your question has already been answered in the comment section, but just to reiterate, you should set the frequency to 24, as you want to forecast the hourly data:

sensor = ts(hourlyPressure, frequency = 24)

To your next point with regards to fixing the dates in your plot, lets start with some example data:

###Sequence of numbers to forecast    
hourlyPressure<-c(1:24, 12:36, 24:48, 36:60)
###Sequence of Accompanying Dates
dates<-seq(as.POSIXct("2016-04-19 00:00:00"), as.POSIXct("2016-04-23 02:00:00"), by="hour")

Now we can set the hourlyPressure data to be a ts() object (let's ignore the dates for a minute)

sensor <- ts(hourlyPressure, frequency=24)

Now fit your arima model, in this example I will use the auto.arima function from the forecast package as finding the best arima model is not the focus of attention here (although using auto.arima() is a pretty robust way of finding the best arima model to fit your data):

###fit arima model to sensor data
sensor_arima_fit<- auto.arima(sensor)

You can then plot this data with the appropriate dates by just specifying the x value in the plot() function

plot(y=sensor_arima_fit$x, x=dates)

A little more difficult is when we forecast our data and want to plot the original data, with the forecasts and have the dates correct.

###now forecast ahead (lets say 2 days) using the arima model that was fit above
forecast_sensor <- forecast(sensor_arima_fit, h = 48)

Now to plot the original data, forecasts with the correct dates, we can do the following:

###set h to be the same as above
h <- c(48)
###calculate the dates for the forecasted values
forecasted_dates<-seq(dates[length(dates)]+(60*60)*(1), 
                  dates[length(dates)]+(60*60)*(h), by="hour")

###now plot the data
plot(y=c(forecast_sensor$x, forecast_sensor$mean), 
     x=seq(as.POSIXct("2016-04-19 00:00:00"),as.POSIXct(forecasted_dates[length(forecasted_dates)]), by="hour"),
     xaxt="n", 
     type="l", 
     main="Plot of Original Series and Forecasts", 
     xlab="Date", 
     ylab="Pressure")

###correctly formatted x axis
axis.POSIXct(1, at=seq(as.POSIXct("2016-04-19 00:00:00"), 
                       as.POSIXct(forecasted_dates[length(forecasted_dates)]), 
                       by="hour"), 
             format="%b %d", 
             tick = FALSE)

This plots the original data with the forecasts and the dates are correct. However, just like the forecast package provides, perhaps we want the forecasts to be in blue.

###keep same plot as before
plot(y=c(forecast_sensor$x, forecast_sensor$mean), 
     x=seq(as.POSIXct("2016-04-19 00:00:00"),as.POSIXct(forecasted_dates[length(forecasted_dates)]), by="hour"),
     xaxt="n", 
     type="l", 
     main="Plot of Original Series and Forecasts", 
     xlab="Date", 
     ylab="Pressure")

axis.POSIXct(1, at=seq(as.POSIXct("2016-04-19 00:00:00"), 
                       as.POSIXct(forecasted_dates[length(forecasted_dates)]), 
                       by="hour"), 
             format="%b %d", 
             tick = FALSE)

###This time however, lets add a different color line for the forecasts
lines(y=forecast_sensor$mean, x= forecasted_dates, col="blue")