**6. Stationary time series**

This can be judged by looking at its time plot. The time plot appears similar at different points along the time axis, and the time series plot is as shown in **Figure 1**. The average daily milk production of a cow (Y) is decreasing over time (t) and is not stationary; we must change the time series plot into a stationary form using the differencing method.

#### **6.1 Stationary through differencing**

After differencing the data in lag two, the data becomes a stationary series, as illustrated in **Figure 2**. This plot shows that the series varies around the mean. This indicates that it does not deviate or drift from the mean, and the time plots appear to be similar in various places. As a result, the time series is stationary, suggesting that the fluctuation in the average daily milk production of cows is not far apart from one another.

#### **6.2 Stationary trend and difference**

The trend analysis plot reveals that it is not stationary, implying that it will require differencing to become stationary. The trend analysis becomes stationary after differencing the data by lag two, as illustrated in **Figure 3**. The amount of average daily milk output is declining, as shown by the fitted trend in **Figure 4**. For

**Figure 1.** *Average volume of milk production (litter).*

*Predicting Trends, Seasonal Effects, and Future Yields in Cow's Milk through Time… DOI: http://dx.doi.org/10.5772/intechopen.105704*

**Figure 2.** *Stationary time series plot.*

**Figure 3.** *Trend analysis.*

**Figure 4.** *Stationary trend analysis.*

179 days of data, the slope of the trend is 16.066, which represents the rate at which the amount of average milk per day is decreasing. This also implies that the average daily milk consumption decreases over time.

### **6.3 Moving average**

**Figure 5** depicts the moving average plot after the data has been transformed into stationary form by differentiating the observations.


*For all those three measures, the smaller value is a better fit for the model, that is, MAD = 81.0 is a better fit for the model.*
