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 39.91% per annum.
- AMAT price at the close of January 17, 2025 was $192.05 and was higher than the top border of the primary price channel by $5.86 (3.15%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 294.34% per annum.
- AMAT price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $0.53 (0.27%).
- 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 15, 2024
End date: January 15, 2025
a = 7.6486
b = -0.0014
s = 0.0609
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0014) – 1
= -39.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0609) – 1
= 27.58%
May 15, 2024 calculations
Top border of price channel:
Exp(Y1,087)
= Exp(a + b × X1,087 + 2 × s)
= Exp(a + b × 1,576 + 2 × s)
= Exp(7.6486 + -0.0014 × 1,576 + 2 × 0.0609)
= Exp(5.5714)
= $262.80
Bottom border of price channel:
Exp(Y1,087)
= Exp(a + b × X1,087 – 2 × s)
= Exp(a + b × 1,576 – 2 × s)
= Exp(7.6486 + -0.0014 × 1,576 – 2 × 0.0609)
= Exp(5.3278)
= $205.98
January 15, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(7.6486 + -0.0014 × 1,821 + 2 × 0.0609)
= Exp(5.2295)
= $186.71
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(7.6486 + -0.0014 × 1,821 – 2 × 0.0609)
= Exp(4.9859)
= $146.34
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 39.91% per annum.
- AMAT price at the close of January 17, 2025 was $192.05 and was higher than the top border of the primary price channel by $5.86 (3.15%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: December 18, 2024
End date: January 17, 2025
a = -1.6557
b = 0.0038
s = 0.0290
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0038) – 1
= 294.34%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0290) – 1
= 12.32%
December 18, 2024 calculations
Top border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 + 2 × s)
= Exp(a + b × 1,793 + 2 × s)
= Exp(-1.6557 + 0.0038 × 1,793 + 2 × 0.0290)
= Exp(5.1422)
= $171.10
Bottom border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 – 2 × s)
= Exp(a + b × 1,793 – 2 × s)
= Exp(-1.6557 + 0.0038 × 1,793 – 2 × 0.0290)
= Exp(5.0261)
= $152.34
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(-1.6557 + 0.0038 × 1,823 + 2 × 0.0290)
= Exp(5.2550)
= $191.52
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(-1.6557 + 0.0038 × 1,823 – 2 × 0.0290)
= Exp(5.1389)
= $170.52
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 294.34% per annum.
- AMAT price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $0.53 (0.27%).
- 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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