Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 37.16% per annum.
- AMAT price at the close of May 16, 2025 was $165.57 and was higher than the top border of the primary price channel by $0.73 (0.44%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1,492.86% per annum.
- AMAT price at the close of May 16, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of AMAT price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: May 14, 2024
End date: May 9, 2025
a = 7.2939
b = -0.0013
s = 0.0663
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -37.16%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0663) – 1
= 30.37%
May 14, 2024 calculations
Top border of price channel:
Exp(Y1,004)
= Exp(a + b × X1,004 + 2 × s)
= Exp(a + b × 1,457 + 2 × s)
= Exp(7.2939 + -0.0013 × 1,457 + 2 × 0.0663)
= Exp(5.5721)
= $262.98
Bottom border of price channel:
Exp(Y1,004)
= Exp(a + b × X1,004 – 2 × s)
= Exp(a + b × 1,457 – 2 × s)
= Exp(7.2939 + -0.0013 × 1,457 – 2 × 0.0663)
= Exp(5.3069)
= $201.72
May 9, 2025 calculations
Top border of price channel:
Exp(Y1,251)
= Exp(a + b × X1,251 + 2 × s)
= Exp(a + b × 1,817 + 2 × s)
= Exp(7.2939 + -0.0013 × 1,817 + 2 × 0.0663)
= Exp(5.1139)
= $166.32
Bottom border of price channel:
Exp(Y1,251)
= Exp(a + b × X1,251 – 2 × s)
= Exp(a + b × 1,817 – 2 × s)
= Exp(7.2939 + -0.0013 × 1,817 – 2 × 0.0663)
= Exp(4.8487)
= $127.58
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 37.16% per annum.
- AMAT price at the close of May 16, 2025 was $165.57 and was higher than the top border of the primary price channel by $0.73 (0.44%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 16, 2025
End date: May 16, 2025
a = -8.6945
b = 0.0076
s = 0.0279
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0076) – 1
= 1,492.86%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0279) – 1
= 11.82%
April 16, 2025 calculations
Top border of price channel:
Exp(Y1,235)
= Exp(a + b × X1,235 + 2 × s)
= Exp(a + b × 1,794 + 2 × s)
= Exp(-8.6945 + 0.0076 × 1,794 + 2 × 0.0279)
= Exp(4.9669)
= $143.58
Bottom border of price channel:
Exp(Y1,235)
= Exp(a + b × X1,235 – 2 × s)
= Exp(a + b × 1,794 – 2 × s)
= Exp(-8.6945 + 0.0076 × 1,794 – 2 × 0.0279)
= Exp(4.8552)
= $128.40
May 16, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(-8.6945 + 0.0076 × 1,824 + 2 × 0.0279)
= Exp(5.1944)
= $180.26
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(-8.6945 + 0.0076 × 1,824 – 2 × 0.0279)
= Exp(5.0827)
= $161.21
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1,492.86% per annum.
- AMAT price at the close of May 16, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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