Objective: to derive fitted value for front-month gold futures prices (dependent variable) based on cross-asset market independent variables. All variables are non-stationary per Augmented Dickey-Fuller testing. I would like this fitted value to represent a price target for investment purposes. I would prefer to use the non-stationary values to keep the original information content as opposed to differencing the data and do regression.

Economic rationale: as a group, collectively, cross-asset market variables should convey information about the price of front-month gold futures. For example, real 10-year U.S. Treasury yields, 10-year U.S. inflation break even inflation rates, Euro-Yen spot exchange rate and Eurodollar futures 12-month/front-month spread proxy for some of the reasons investors would own gold (i.e., general risk aversion, deflation hedge, inflation hedge, monetary policy view). As such they could help isolate some idiosyncratic factor being priced into gold futures, such as speculative euphoria, which could show up as a high residual.

Dependent variables: daily time series of gold front-month futures closing prices since January 1st, 2010.

Independent variables: daily real 10-year U.S. Treasury yields, 10-year U.S. inflation breakeven rates, Euro-Yen currency spot rate and Eurodollar futures 12-month/front-month spread closing values since January 1st, 2010.

Data: daily closing values since January 1st, 2010, non-stationary (i.e., level) data.

What I've tried so far: using statistical package XLSTAT in Excel I've used linear regression based on non-stationary variables described above. The r-square is high (0.77) and standardized residuals are non-stationary. Although I'm not an econometrician, I've read that the high r-square is bogus because the regression residuals are non-stationary based on ADF and KPSS tests, meaning that there is no cointegrative relationship between the dependent and independent variables, although Phillips-Perron test finds the residuals stationary. That said, I struggle to understand what's wrong with this approach as I'm regressing what are, based on economic theory, not really independent processes (i.e., gold prices should be, to some extent, dependent on real 10-year rates as investors hedge deflation risk) so I would expect them to trend together.

Below are some of the outputs from this model and a link to the Excel file with the raw data. Link to raw data: https://www.dropbox.com/sh/frzkuv5goutuxn7/AAC7_3IgOC0YA25g8-dD38uTa?dl=0

Graphical outputs:

1) The r-square:

2) 2) The actual versus fitted output:

3) The standardized residuals: