title: Forecasting 5 Day Sales
body: <p>I have daily sales data between 2013-02-18 to 2017-02-12 that has only 4 days of data missing (all the Xmases on the 25th of each year). These holidays have a sale volume of zero. <strong>My purpose is to understand how to staff my store for the upcoming week by short-term predicting my sales for the next 5-7 days worth of data.</strong></p>
  
  <p>I start by setting up this data as a time series: </p>
  
  <pre><code>ts &lt;- ts(mydata, frequency = 365)
  </code></pre>
  
  <p>and then an initial analysis through a decomposition:</p>
  
  <p><a href="https://i.stack.imgur.com/EKtqG.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/EKtqG.png" alt="Decomposition of daily data between 2013-02-18 to 2017-02-12"></a></p>
  
  <p>This seems to show I have a declining sales trend, but there is some seasonality, if I'm not mistaken. So, to start my forecast implementation, I  fit an arima model for the first two years worth of data by doing:</p>
  
  <pre><code>fit &lt;- auto.arima(ts[1:730], stepwise = FALSE, approximation = FALSE)
  
  Series: ts[1:730] 
  ARIMA(4,1,1)                    
  
  Coefficients:
           ar1      ar2      ar3      ar4      ma1
        0.3638  -0.2290  -0.1451  -0.2075  -0.8958
  s.e.  0.0413   0.0388   0.0388   0.0398   0.0241
  
  sigma^2 estimated as 15424930:  log likelihood=-7068.67
  AIC=14149.33   AICc=14149.45   BIC=14176.88
  </code></pre>
  
  <p>This model doesn't seem right to me, because it does not include any seasonality. I know I have enough data. Rob Hyndman's blog said to try using <code>ets</code> which also showed no seasonality. What am I not understanding about this data series or the forecasting methodology?</p>