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I have a time Series data like

patients: 100, 200, 300,...,10, 5,...,120
Month:     1,  2 ,  3 ..., 12, 1,...,12    
Year:     2006,2006,2006,...,2006,2007,..,2007  

Like this I have data till 2010, I need to predict patients for 2011

I wanted to check for the trend in the data, so I used below ggplot to plot the trend line. When I used only "geom_smooth()" I got a exponential curve line based on loose() and when I use geom_smooth(method="lm"). I got a straight line. My question is which one is correct?.

A. I have TS and from both the graphs I see I only have a trend and no seasonality(which is correct). For fitting TS data which one is correct?

geom_smooth() geom_smooth(method="lm")

ggplot(data,aes(x= Year,y=Incoming.Examinations))+ geom_point(aes(color=Month))+
    geom_smooth() #geom_smooth(method="lm") 

imputed<- mice(data)
imputed$imp
fit <- with(imputed,ets(Incoming.Examinations,model="AAN"))
#fit <- pool(fit)
fit
completedData<-complete(imputed,4)
fit<-ets(completedData$ts,model="AAN")
y<-predict(fit,n.ahead=15)

B. I had missing values in the "patients",so, I used mice package to impute the missing values. As I only have trend, I decided to use Double exponential smoothing in

with(imputed,ets(Incoming.Examinations,model="AAN"))

using ets(). Now, the problem is

fit <- pool(fit)

gives me an error

Error: No glance method for objects of class ets

looks like pool works only with lm, glm in with(). B.1 How do I fix this?

B.2 As a work around,I dumped fit and checked all the results and picked the dataset 4 with low AIC and predicted the output. is this right thing to do? or is it mandatory to use the pool(fit) and then make a decision?

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For A, you can simply use RMSE to compare both trend lines to see which one has the smaller RMSE. Obviously by looking at the graph, the trend line produced by loose() option should be the better one.

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