Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 64.29% per annum.
- AMAT price at the close of May 20, 2024 was $219.95 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 121.20% per annum.
- AMAT price at the close of May 20, 2024 was inside the secondary price channel.
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: August 30, 2022
End date: May 20, 2024
a = 2.8397
b = 0.0014
s = 0.0747
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 64.29%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0747) – 1
= 34.81%
August 30, 2022 calculations
Top border of price channel:
Exp(Y826)
= Exp(a + b × X826 + 2 × s)
= Exp(a + b × 1,197 + 2 × s)
= Exp(2.8397 + 0.0014 × 1,197 + 2 × 0.0747)
= Exp(4.6171)
= $101.20
Bottom border of price channel:
Exp(Y826)
= Exp(a + b × X826 – 2 × s)
= Exp(a + b × 1,197 – 2 × s)
= Exp(2.8397 + 0.0014 × 1,197 – 2 × 0.0747)
= Exp(4.3184)
= $75.07
May 20, 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(2.8397 + 0.0014 × 1,826 + 2 × 0.0747)
= Exp(5.4726)
= $238.09
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.8397 + 0.0014 × 1,826 – 2 × 0.0747)
= Exp(5.1739)
= $176.61
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 64.29% per annum.
- AMAT price at the close of May 20, 2024 was $219.95 and was inside the primary price channel.
Secondary Trend
Start date: September 20, 2023
End date: May 20, 2024
a = 1.4284
b = 0.0022
s = 0.0533
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0022) – 1
= 121.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0533) – 1
= 23.76%
September 20, 2023 calculations
Top border of price channel:
Exp(Y1,091)
= Exp(a + b × X1,091 + 2 × s)
= Exp(a + b × 1,583 + 2 × s)
= Exp(1.4284 + 0.0022 × 1,583 + 2 × 0.0533)
= Exp(4.9781)
= $145.20
Bottom border of price channel:
Exp(Y1,091)
= Exp(a + b × X1,091 – 2 × s)
= Exp(a + b × 1,583 – 2 × s)
= Exp(1.4284 + 0.0022 × 1,583 – 2 × 0.0533)
= Exp(4.7649)
= $117.32
May 20, 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(1.4284 + 0.0022 × 1,826 + 2 × 0.0533)
= Exp(5.5066)
= $246.32
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.4284 + 0.0022 × 1,826 – 2 × 0.0533)
= Exp(5.2934)
= $199.03
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 121.20% per annum.
- AMAT price at the close of May 20, 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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