My dissertation aims at developing econometric tests to study nonstationarity in panel data allowing for cross-correlations. The first chapter examines excessive comovement and nonstationarity in commodity prices. Pindyck and Rotemberg (1990) found excessive comovements among prices of a broad set of commodities. Wang and Tomek (2007) argue that commodity prices should be stationary and convergent though literature shows otherwise. I use both the principal component analysis (PCA) and dynamic factor models (DFM) to extract the comovements. We find some comovements, but they are not excessive. Then I control for the common factors and structural breaks in our unit root tests. I show that most commodity prices are non-stationary even after accounting for comovements and structural breaks. The second chapter studies the Prebisch-Singer (PS) hypothesis implying that commodity prices decline relative to industrial prices over the time. This has important implications for the growth of developing countries though the empirical evidence on the hypothesis is mixed. Using the dynamic factor models and principal component analyses I find significant comovements. I employ the residual augmented least squares (RALS) procedure to utilize the information contained in those factors and in the non-normal errors. I use Fourier function to model structural changes. Using data from 1900 to 2018, I find significantly negative trend in the common Fourier function and the dynamic common factor of the relative prices which supports the PS hypothesis. Out of the 24 individual relative commodity prices, I find negative trend in 12, positive trend in 6 and no clear pattern in others. I find an emerging positive trend in several of them from early 2000s. The last chapter develops a new unit-root test that accounts for dummy breaks and factors extend the two break tests of Lee and Strazicich (2003) in a factor structure to allow for cross-correlations using the PANIC procedure of Bai and Ng (2004). Then, we apply the new tests to examine the stochastic convergence of carbon dioxide (CO2) emissions for a set of 30 OECD countries during the period 1960-2018. Our results show that the null of no convergence is rejected only for a few countries.