Consider the following dynamic factor model: $\mathbf{R}_t=\sum_{i=0}^q \mathbfΛ_i \mathbf{f}_{t-i}+\mathbf{e}_t,t=1,...,T$, where $\mathbfΛ_i$ is an $n\times k$ loading matrix of full rank, $\{\mathbf{f}_t\}$ are i.i.d. $k\times1$-factors, and $\mathbf{e}_t$ are independent $n\times1$ white noises. Now, assuming that $n/T\to c>0$, we want to estimate the orders $k$ and $q$ respectively. Define a random matrix $$\mathbfΦ_n(τ)=\frac{1}{2T}\sum_{j=1}^T (\mathbf{R}_j \mathbf{R}_{j+τ}^* + \mathbf{R}_{j+τ} \mathbf{R}_j^*),$$ where $τ\ge 0$ is an integer. When there are no factors, the matrix $Φ_{n}(τ)$ reduces to $$\mathbf{M}_n(τ) = \frac{1}{2T} \sum_{j=1}^T (\mathbf{e}_j \mathbf{e}_{j+τ}^* + \mathbf{e}_{j+τ} \mathbf{e}_j^*).$$ When $τ=0$, $\mathbf{M}_n(τ)$ reduces to the usual sample covariance matrix whose ESD tends to the well known MP law and $\mathbfΦ_n(0)$ reduces to the standard spike model. Hence the number $k(q+1)$ can be estimated by the number of spiked eigenvalues of $\mathbfΦ_n(0)$. To obtain separate estimates of $k$ and $q$ , we have employed the spectral analysis of $\mathbf{M}_n(τ)$ and established the spiked model analysis for $\mathbfΦ_n(τ)$.