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In a Periodic Double Auction (PDA), there are multiple discrete trading periods for a single type of good. PDAs are commonly used in real-world energy markets to trade energy in specific time slots to balance demand on the power grid. Strategically, bidding in a PDA is complicated because the bidder must predict and plan for future auctions that may influence the bidding strategy for the current auction. We present a general bidding strategy for PDAs based on forecasting clearing prices and using Monte Carlo Tree Search (MCTS) to plan a bidding strategy across multiple time periods. In addition, we present a fast heuristic strategy that can be used either as a standalone method or as an initial set of bids to seed the MCTS policy. We evaluate our bidding strategies using a PDA simulator based on the wholesale market implemented in the Power Trading Agent Competition (PowerTAC) competition. We demonstrate that our strategies outperform state-of-the-art bidding strategies designed for that competition.