Analysis of Time Series data The below graph is a scatterplot of daily stock price. My aim is to predict future stock price of the company.

From the scatterplot it seems that it is a multiplicative model, so I tried to "decompose" it in R. However it says that "time series has no or less than 2 periods". I also obtained a periodogram, which has only one peak at frequency close to 0.



However, my teacher told me that this time series cannot have a trend therefore to eliminate the seasonality I have to consider its period as 7 and then eliminate it choosing an appropriate model. 
Can anyone tell me what could be an appropriate model along with a proper justification? Also is it true that the series cannot have a trend?
Speaking as someone from a finance background, the `usual' model for a stock price process is

$\frac{dS}{S}=r dt + \sigma dW_t$

i.e. we assume the returns (not the absolute price changes, i.e. dS/S is approximately the daily percentage change in price) as having a 'drift' equal to the risk free rate (the interest rate r) and a random shock $dW_t$ with standard deviation $\sigma$

So it's basically the opposite of what you've been asked, I would expect a trend (but it's very hard to estimate with confidence) and I would not expect any seasonality, you could fit an arithmetic model by taking the daily differences though.