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 10.84% per annum.
- AMAT price at the close of March 27, 2024 was $208.00 and was higher than the top border of the primary price channel by $82.92 (66.30%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 61.97% per annum.
- AMAT price at the close of March 27, 2024 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: January 11, 2021
End date: May 16, 2023
a = 5.1141
b = -0.0003
s = 0.1443
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.84%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1443) – 1
= 78.10%
January 11, 2021 calculations
Top border of price channel:
Exp(Y451)
= Exp(a + b × X451 + 2 × s)
= Exp(a + b × 655 + 2 × s)
= Exp(5.1141 + -0.0003 × 655 + 2 × 0.1443)
= Exp(5.1969)
= $180.70
Bottom border of price channel:
Exp(Y451)
= Exp(a + b × X451 – 2 × s)
= Exp(a + b × 655 – 2 × s)
= Exp(5.1141 + -0.0003 × 655 – 2 × 0.1443)
= Exp(4.6197)
= $101.46
May 16, 2023 calculations
Top border of price channel:
Exp(Y1,041)
= Exp(a + b × X1,041 + 2 × s)
= Exp(a + b × 1,510 + 2 × s)
= Exp(5.1141 + -0.0003 × 1,510 + 2 × 0.1443)
= Exp(4.9282)
= $138.13
Bottom border of price channel:
Exp(Y1,041)
= Exp(a + b × X1,041 – 2 × s)
= Exp(a + b × 1,510 – 2 × s)
= Exp(5.1141 + -0.0003 × 1,510 – 2 × 0.1443)
= Exp(4.3510)
= $77.56
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.84% per annum.
- AMAT price at the close of March 27, 2024 was $208.00 and was higher than the top border of the primary price channel by $82.92 (66.30%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: August 29, 2022
End date: March 27, 2024
a = 2.8230
b = 0.0013
s = 0.0763
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 61.97%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0763) – 1
= 35.68%
August 29, 2022 calculations
Top border of price channel:
Exp(Y862)
= Exp(a + b × X862 + 2 × s)
= Exp(a + b × 1,250 + 2 × s)
= Exp(2.8230 + 0.0013 × 1,250 + 2 × 0.0763)
= Exp(4.6272)
= $102.22
Bottom border of price channel:
Exp(Y862)
= Exp(a + b × X862 – 2 × s)
= Exp(a + b × 1,250 – 2 × s)
= Exp(2.8230 + 0.0013 × 1,250 – 2 × 0.0763)
= Exp(4.3221)
= $75.34
March 27, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.8230 + 0.0013 × 1,826 + 2 × 0.0763)
= Exp(5.3882)
= $218.81
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.8230 + 0.0013 × 1,826 – 2 × 0.0763)
= Exp(5.0831)
= $161.27
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 61.97% per annum.
- AMAT price at the close of March 27, 2024 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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