**2. Data and methods**

This study was conducted at Andassa dairy farm, which is located in the Amhara region in northwestern Ethiopia. At Andassa dairy farm, milk production was recorded in liters per cow on a daily basis. This study employed only secondary data obtained from this dairy sector.

### **2.1 Statistical method**

A time series is a set of ordered observations of quantitative variables taken at successive points in time. In other words, it is a set of observations recorded over time, which is usually at equal intervals. Stationary is a critical assumption in time series models. Stationary implies homogeneity in the sense that the series behaves in a similar way regardless of time, which means that its statistical properties do not change over time. Trend analysis is the characteristics of a time series that extends consistently throughout the entire period of time under consideration. In this scenario, trend analysis was used to anticipate the future amount of milk products based on the historical trend of milk production. In this case, we will look at a linear trend and estimate it using the least square estimation method, double moving average, and double exponential smoothing [6].

#### **2.2 Autocorrelation function and partial autocorrelation function**

The two moments of any random variable, namely its mean and variance, are well known, and since we established in the introduction that a time series is a realization of a stochastic process, this holds true for any time series. In Box–Jenkins model, the partial autocorrelation plot or partial correlogram is also often employed for model identification [7].

### **3. ARMA model**

The ARMA model is a mixed model in which the series is partly autoregressive and partly moving average. As a result, we get a very generic time series model, as shown below.

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

*Yt* ¼ Φ1*Yt*�<sup>1</sup> þ Φ2*Yt*�2<sup>þ</sup> ……… Φ*pYt*�*<sup>p</sup>* þ *et* þ *et*–Ɵ1*et*�1–Ɵ2*et*�<sup>2</sup> … … *::*–Ɵ*qet*�*<sup>q</sup>*

We say that {*Yt*} is a mixed autoregressive moving average process of order p and q, respectively. We abbreviate the name to ARMA (p, q).
